We have no idea: it's never addressed by the show.
However, the assumption that only a TARDIS could let the Master escape to the end of the universe is erroneous.
Lest we forget, the Last Great Time War wouldn't have been a time war if the Daleks hadn't also possessed time travel technology. Many of the more advanced societies of the Whoniverse do--or did, or will; it gets confusing. Even Captain Harkness has a Time Wristband. The Master could well have hijacked or hitchhiked from another race, or used non-TARDIS Gallifreyan time travel tech. Some time travel is more like "opening a hole" or a "time cannon" than a machine, which would leave no tech at the destination; or if he hitched a ride, the driver would leave after dropping him off. Or if the Master used his TARDIS or stole a machine, he may have destroyed it to make it harder for him to be found (I'd guess that the Master was canny enough not to effect his escape using a vessel capable of streaming all events in and around itself to Gallifrey High Command in the first place).
Or maybe his TARDIS is still out there, but he stole the Doctor's because it was closer and safer to get to --and because doing so would, he hoped, strand the Doctor.
But again, this is all pure rampant speculation with absolutely no support or evidence. The show--and to the best of my knowledge all non-show story material--is silent on the matter.