With Perl 5.18.2 on a Ubuntu 14.04 box I don't seem to get any error if I replace the double quotes for single quotes around the code, but when I try to reproduce the behavior in the cases you report (a.k.a escaping the brace or leaving it unescaped ) I get the following error

perl -le "$_=~/sub mymy\{}/;"

syntax error at -e line 1, near ";=~"
Execution of -e aborted due to compilation errors.
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The error is consistently reported in all the cases you mentioned in your follow-up reply too