I had to read this a few times to understand it, but I think you're asking how long someone stays on the enemy's map for after they've stopped sprinting?
If that's it, then their dot leaves the map a second or so after they stop sprinting. But the point is they've already given away the direction (if not exact position) because of that sprinting. A lot of players don't seem to realize this, and they don't seem to realize that you don't show up on the map if you simply walk. Instead, they sprint to a box, then crouch behind it and pretend to be stealth, not realizing they've alerted the enemy team to their position (and thus aren't stealth).
As for showing up on the wall hack, yes you show up if you're walking or crouch walking (unless you're using the highest stealth perk, then crouch walking is invisible), but that's in the situation where an enemy already knows to "listen" since you or a team-mate is close by. And again, the enemy starts listening in the first place a lot of the time because someone on the other team has sprinted for no reason.