Disappeared.
Probably kept killing until stopped. Perhaps he was arrested on another crime or died an otherwise early death.
A year or so ago, one of the cable channels had a documentary called "American Ripper". It was about an American who was convinced that a relative of his was actually Jack the Ripper.
After watching this show, I was pretty well convinved that this mans relative was Jack the Ripper.
One of the reasons I decided he was a good fit for the Ripper was that when the Ripper killings stopped, this guy, H.H. Holmes, was on a ship back to the States. He was an American Medical Student doing an internship in London. Shortly after the date he arrived back in NYC, a string of "ripper like" murders began to occur.
He moved around a lot, and he was in Chicago during the World's Fair, when many young women simply disappeared while attending the Fair. He had bought a hotel and redesigned the inside so that he could murder someone (with gas), then easily get the body down to the basement where he would dissect them. The hotel was later dubbed, "The Murder Hotel".
It was an interesting show on the subject, though a bit repetitious.