How would you know if your tubes had become untied?

Pregnancy. Having tubal sterilization is not like tying your laces where they can be "untied". Tubal sterilization usually is performed by damaging a portion of the tube with electrocoagulation, placement of clip/ring, or removal of portion of the tube. When treatement failure occurs (~2% over 10-year period), it usually occurs as fistulas or small openings occur, not because the preocedure is reversed.
X Ray. You can have an X-ray performed (hsg - hysterosalpingogram) to confirm if the tubes are still blocked. Unfortunately some women also find out when they become pregnant unexpectedly.