Does anyone know how to make a field be accessible for data entry, but then once FileMaker is closed, that data becomes non-deletable next time the program is open. But then you can add more data in the same field, just not delete what was there previously?

The simplest way I can think of is to enter the data into a global field 'gMyDataEntryField' and then click a button that performs a one line script:

Set Field [TextField, TextField & "

An alternative way to approach this would be to set up a closing script which copies the contents of the field to a separate field (one that doesn't appear on the layout, then specify a validation-by-calculation for the existing field, along the lines of:

Left(ExistingField, Length(NewField)) = NewField

Then make the validation strict and enter an appropriately explanatory warning message.

Users will then be prevented from proceeding if they have made changes to the original text (and will either have to use the option to revert the field, or manually reverse their changes to the pre-existing text before being able to leave the field).