In Scotland Yard, if Mr. X ever occupies the same location as a detective, he loses on the spot, regardless of if it was by the detective's move or his own move (forced as it may be). This is explicitly mentioned in the Scotland Yard rules, and Scotland Yard does not explicitly allow a double-move to bypass this (so implicitly, you still lose if you do a double-move that passes through a detective's location). This game also doesn't seem to permit Mr. X to remain in a location, noting that Mr. X effectively has an unlimited ticket supply (in theory, it is possible that Mr. X could end up unable to move, but such a situation requires deliberate actions on both the detectives' parts as well as Mr. X's that it should never come up in normal play)
From what I can get of the rules for the game you're specifically asking about, N.Y. Chase, it does not appear to specifically indicate this as a game end, only that if a detective moves to the station that Mr. X is at or if all routes away from Mr. X's location are blocked. Unlike in Scotland Yard, N.Y. Chase's rules account for the possibility that Mr. X may lack the ability to move due to not having appropriate tickets. If Mr. X has options that he cannot take due to not having the tickets, he announces that he has to remain where he is, but the detectives must still locate or completely trap him to win.
