while (s/\s*$RE$//) {}

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or 
s/(\s*$RE)*$//;

[download]
will get you there without leaving trailing spaces in the finished $_. (Update: made it a little easier to read.)

In reply to Re: regexp - repeatedly delete words from end of string with words in alternation by gamache
in thread repeatedly delete words expressed in alternation from end of string [regexp] by princepawn

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