The undef $_++ vs $$_++ I think the former is working because what's happening is:

• An SVrv pointing to the SV* for undef is pushed on the arg stack
• When map calls the EXPR $_++ that reference is getting numified, incremented, and that new int value stuck back into the SV* on the arg stack
• Since it's a postincrement the map is returning the original value of $_ which is the ref to undef
• The call stack goes away and with it the SV* which had the numified address plus one.

In the second case you're explicitly dereferencing the SVrv to the constant undef and trying to increment that (which fails because undef is a singleton readonly SV*).

Edit: And again yes making explanation by way of the implementation, but I think that's because knowing (sort of) how this is implemented under the covers makes these particular corner cases' behaviors not (as) surprising.