Green’s Dictionary of Slang

pad v.3

also pad down
[pad n.2 (2)]

(US black) to live somewhere; to accompany someone.

[UK]R.A. Norton Through Beatnik Eyeballs 40: He done had one witch who pad down with him some months.
[US]‘Iceberg Slim’ Pimp 111: I had told her to work just the block where we padded.
[UK]B. Hare Urban Grimshaw 310: Skeeter and Frank were recently padded up together in the same jail.
[UK]J.J. Connolly Viva La Madness 25: Me and Sonny in the rental, Roy and Morty padded up together.