Yes, I don't know if the regex reached the end of the string and failed, in which case I'd have to load more data.

If the match test fails then you have reached the end of the string without a match, unless the regex begins with a '^'. If you disallow this, you should be fine:

 $str="";
 while(<>){
   $str.=$_;
   last if (m/a\d+b/g);
 }
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The end of the string could be a partial match at the end, but you don't care, because the next string catenation will either allow a match, or discard it (depending on what the new data turns out to be).

The previous ugly example is most likely the only other solution. It may not be as cpu-expensive as you think. Since each iteration is anchored at the end-of-string, it will not match against the whole string in general. The invalid regex's will bail immediately, without matching a thing.