I have been in contact with my association (no unions for teachers in Texas)
and the lawyer I talked to said there was no compelling reason to send my
district the resignation since there is no professional slight to getting
terminated in a RIF the district conducts for financial exigency. It's just
what HR said all along- that some people don't like the word "terminated" and
will want to keep it off their record if they can. Thanks for all the replies,
though.