Make sure both 1 and 19978 exist in parent table, insert if not.

Update the child table, it will now pass without error.

Delete the old parent row.

I hope it is not your regular procedure, because updating primary key which is by default also a clustered index key, is a very bad idea because of fragmentation and slow operation.

If it is your regular operation, you should create new IDENTITY field and make that a primary key, and reference that with FK constraint.

That will not change and you will not have all sorts of problems you now have.