It’s a metal vertical travel shutter.
Yes, I was sloppy in saying "second curtain," but if I'd said closing set of blades, it would have all been correct. I do have a box of Nikkormats, most of which work (Nikkormats are very durable), but a few have problems like I described, for example sticking open at the slowest speeds, where moving the shutter dial to a faster speed will usually close the shutter.
Typically the mechanical chain is such that the mirror goes up, then allowing the shutter to open, then the shutter closes, triggering the mirror to go down. The Nikkormat has mirror lockup, so there has to be a mechanical action that closes the blades even if the MLU is engaged and the mirror is physically up.
Here is a little experiment to show that the Nikkormat mirror being up does not cause the shutter to hang open. Put the camera on B, no lens, no mirror lock-up and DO NOT DO THIS UNLESS YOU ARE VERY CAREFUL. Fire and hold the shutter and while the mirror is up, put your finger gently on the front edge of the mirror to hold it up. Let go the shutter release and the shutter will close even though you are holding the mirror up. You can even do this on 1 sec instead of B if you are fast. Anyway, that's why I don't think sticky foam is an issue here. The problem is a sticky or out of sync shutter mechanism.
I agree with Sirius that putting your finger on a shutter or in the path of a shutter is a good way to wreck it.