You have the ability to prevent the hide.bs.modal event from occurring if certain conditions are met.

$("#exampleModal").on("hide.bs.modal", function(event) {
  if (!document.querySelector("#defaultCheck1").checked) {
    event.preventDefault();
  }
});

<script src="https://cdn.jsdelivr.net/npm/<a href="/cdn-cgi/l/email-protection" class="__cf_email__" data-cfemail="d2b8a3a7b7a0ab92e1fce7fce3">[email protected]</a>/dist/jquery.slim.min.js" integrity="sha384-DfXdz2htPH0lsSSs5nCTpuj/zy4C+OGpamoFVy38MVBnE+IbbVYUew+OrCXaRkfj" crossorigin="anonymous"></script>
<script src="https://cdn.jsdelivr.net/npm/<a href="/cdn-cgi/l/email-protection" class="__cf_email__" data-cfemail="cdafa2a2b9beb9bfacbd8df9e3fbe3ff">[email protected]</a>/dist/js/bootstrap.bundle.min.js" integrity="sha384-Fy6S3B9q64WdZWQUiU+q4/2Lc9npb8tCaSX9FK7E8HnRr0Jz8D6OP9dO5Vg3Q9ct" crossorigin="anonymous"></script>

<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/<a href="/cdn-cgi/l/email-protection" class="__cf_email__" data-cfemail="31535e5e45424543504171051f071f03">[email protected]</a>/dist/css/bootstrap.min.css" integrity="sha384-xOolHFLEh07PJGoPkLv1IbcEPTNtaed2xpHsD9ESMhqIYd0nLMwNLD69Npy4HI+N" crossorigin="anonymous">

<!-- Button trigger modal -->
<button type="button" class="btn btn-primary" data-toggle="modal" data-target="#exampleModal">
  Launch demo modal
</button>

<!-- Modal -->
<div class="modal fade" id="exampleModal" tabindex="-1" aria-labelledby="exampleModalLabel" aria-hidden="true">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <h5 class="modal-title" id="exampleModalLabel">Modal title</h5>
        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
          <span aria-hidden="true">&times;</span>
        </button>
      </div>
      <div class="modal-body">
        <div class="form-check">
          <input class="form-check-input" type="checkbox" value="" id="defaultCheck1">
          <label class="form-check-label" for="defaultCheck1">
    Allow Closing
  </label>
        </div>
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>

      </div>
    </div>
  </div>
</div>

To avoid using the "close" function, incorporate a Subject into your modal component and subscribe to it when opening. The responsibility of closing the popup lies with the component that opened it.

//inside your modal component
    @Input() form: FormGroup;
    submit:Subject<any>=new Subject<any>()

//in .html
<div class="modal-header">
  <h4 class="modal-title"gt;Hi there!</h4>
  <button type="button" class="btn-close" aria-label="Close"
           (click)="activeModal.dismiss()"
  ></button>
</div>
<div class="modal-body">
  <p>Hello, {{ name }}!</p>
  <!--A simple form example-->
  <div [formGroup]="form">
    <input formControlName="name" />
  </div>
</div>
<div class="modal-footer">
  <button
    type="button"
    class="btn btn-outline-dark"
    <!--only emit one value to the "submit" subject -->
    (click)="submit.next(form.value)"
  >
    Close
  </button>
</div>

For opening:

  open() {
    const modalRef = this.modalService.open(NgbdModalContent);
    modalRef.componentInstance.name = 'World';
    modalRef.componentInstance.form = this.form;
    modalRef.componentInstance.submit
      .pipe(takeUntil(modalRef.closed))
      .subscribe((data: any) => {
        //Utilize a service that returns true or false
        this.dataService.checkData(data.name).subscribe((res: any) => {
          if (res) modalRef.close(); //this closes the popup
        });
      });
  }

View a stackblitz for reference (popup closes only if you input "Angular" as the name)

Tip: Add details on why the "form" is invalid or consider implementing a custom async validator.

Update: In ngb-popup, subscription can be done within the "show" function:

this.ModalService.show((DynamicFormComponent), config, options).subscribe(...)

Alternatively, store the reference in a variable and then subscribe:

//obtain a reference to the "popup"
const modalRef = this.ModalService.show((DynamicFormComponent), config, options)

//Subscribe to it
modalRef.subscribe(...)

Prefer using the second method mentioned above.

If we define a public variable in our "DynamicFormComponent", it becomes accessible. Hence, add the following variable:

submitSubject:Subject<any>=new Subject<any>()

This enables us to subscribe to the Subject:

//use takeWhile to unsubscribe when the modal closes
modalRef.componentInstance.submitSubject.subscribe((data: any) => {}

Avoid using "close" in DynamicFormComponent. Instead, emit a value to the subject:

 //replace in .html
 (click)="activeModal.close(value)"
 //with
 (click)="submitSubject.next(value)"

All code previously under subscription when closing should now be used within the subscription of the subject. Remember, manual closure of the popup is necessary if all conditions are met:

modalRef.close();

Update:

openModal(rowData: any = null) {
    const config: Partial<DynamicFormComponent> = {
        form: this.form,
        data: rowData
    };

    const options: NgbModalOptions = { size: 'sm', centered: true };

    const modalRef = this.ModalService.show((DynamicFormComponent)
                                                  , config, options)

    modalRef.componentInstance.submitSubject.subscribe((data: any) => { 
       //call API to add the foodItem    
       this.api.request('foodItem', 'POST', data).subscribe({
          next: (response: any) => {
            if (response.message == 'Added Successfully.') {
                this._toastService.showSuccess('Food added.');

                //close after adding
                modalRef.close(); 

                //emit update or insert event
                if (rowData) {
                     const updatedRowData = { ...rowData, ...result.Data };
                     this.onEdit.emit(updatedRowData);
                } else { 
                     this.onAdd.emit(result.Data);
                }


            } else {
                this._toastService.showError(response.message);
            }
          },
          complete: () => this.getFood(),
          error: (error: any) => 
           this._toastService.showError(error.message)
      });
  }

Unfortunately, the question is not directly related to ngb-bootstrap but rather a third-party library.

It appears that this library internally uses ngb-bootstrap, so we can attempt the following to obtain the instance:

private ngbmodalService = inject(NgbModal); //<--inject the NgbModal
//or
private ngbmodalService=this.ModalService as NgbModal
private modalRef:any;                    //declare a variable instance

//subscribe to ngbmodalService.activeInstances
//to assign a value to the "modalRef" variable
activeSubscription=this.ngbmodalService.activeInstances.subscribe(res=>{
  this.modalRef=res.length?res[0]:null
})

This way, when opening:

this.ModalService.show(...)
setTimeout(()=>{
this.modalRef.componentInstance.submitSubject.subscribe(...)
})

And when closing:

this.modalRef.close() //<--close all popups

NOTE: To discover the public properties of an Object, you can use something like:

for (let key in this.ModalService) 
console.log(key)

Or simply:

console.log(this.ModalService)

To understand the "properties" of the Object this.ModalService

Update: Another approach using ViewChildren is to declare in our component:

@ViewChildren(DynamicFormComponent) dinamics:QueryList<DynamicFormComponent>
subscription=this.dinamic.changes(res=>{
console.log(res.length,res.first,(res.first as any).submitSubject)
})

We can attempt to access the DynamicFormComponent and the "submitSubject"