A good waxer most definitely does NOT leave any strays- also, they should never wax the same area twice. Mine will wax an area, then go back and tweeze all the big long hairs the wax didn't get. I still have a few thin blonde hairs to take care of when I get home, but that's only because my waxer couldn't see them under the bright lights she uses.
Shop around for a good waxer squishor, cause it sounds like yours isn't very good

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Sage knows our mythic history, King Arthur's and Sir Caradoc's
She answers hard acrostics, has a pretty taste for paradox
She quotes in elegiacs all the crimes of Heliogabalus
In conics she can floor peculiarities parabolous
-C'hi