Yeah, my preference would also be to just upgrade to stretch. Just upgrading OpenSSL on jessie could be a pain with all dependencies that come with it and could break other things.
The newer OpenSSL versions somehow don't throw a SIGILL anymore on the initialization part to determine the processors capabilities. So it's fixed with those newer versions. It's not something that can be changed in FPC anyway. For this particular combination of GDB debugger and OpenSSL 1.0.1t the only option is to tell it what processor it's dealing with (with the given environment setting).
With 1.0.1t becoming older and older it's just a matter of time until jessie itself (with that version) is so outdated it doesn't work anymore with the newer ssl/tls protocols, like you said, and upgrading becomes inevitable.