Why would you not receive upstream bug fixes with statically linked programs? Assuming you are using an Apt-style package manager then the statically linked program would be rebuilt and updated too.

If you are not using an apt-style package manager then the program must include all of its dependencies (except ones that are guaranteed to be present on the platform, which is none on Linux and a few on Mac/Windows), and you will receive bug fixes when that program is updated, whether or not it uses static linking.

Static/dynamic linking does not affect how likely you are to get bug fixes in any way as far as I can tell.