Starting with 1.1.1c (i.e. 1.1.1b worked fine), when trying to build a non-dynamically-linked image via the -static option, the executable produced (at least under linux) core dumps immediately.

git checkout OpenSSL_1_1_1c
./config -static
make
apps/openssl version

This worked fine under OpenSSL 1.1.1b. The workaround is to add some options that need to be disabled:

git checkout OpenSSL_1_1_1c
./config -static no-shared no-pic no-threads
make
apps/openssl version

It appears that the fix for #8787 (commit 0072137) broke this, based on my git bisect. As far as I can tell, the setting of some of the $disables{} occurs too late with that change. I have yet to figure out the solution, but I wanted to report it before I forgot about it.