Question:
You have a runner on 1st leading off, batter swings and foul tips the ball into the catcher's mitt, but it is dropped and it's not strike three. The runner steals second. Must he return to first?

Coach Will

Foul Ball - runner must return

No catch, no foul tip.

2.00 A FOUL TIP is a batted ball that goes sharp and direct from the bat to the catcher's hands <b>and is legally caught</b>.

Therefore it is a foul ball.

Digging a little deeper.. Same runner on 1st, 2 strikes on batter, batter swings at next pitch, which bounces off the catchers mitt into his mask/chestprotector and the catcher traps the ball on his chest protector with his mitt before the ball touches the ground. Foul ball, right? Is the batter out? Must the runner tag up before going to 2nd?

TIA

Nice question
 

Off his mitt and then caught...? That's a foul tip (because it hit the mitt first) and a catch. Runner can advance and batter is out.

Check your case book 2.16.1 COMMENT (4)
A pitch touches the bat of B2 in (a), it goes directly to F2's glove, then into his protector and rebounds into his hand or glove or (b)it goes directly to F2's protector or mask and rebounds into his hand or glove. In (a), it is a foul tip and a catch. In (b), the ball becomes dead when it touches the body of F2 and is an uncaught foul. In a related situation, a foul ball rises (emphasis mine) and comes down to strike the catcher's mask or protector and then rebounds into his hand. It is a caught foul. B2 is out and the ball remains alive. (5-1-1d. 7-2-1d)

Checking the definition of a foul tip... 2-16-2
... a batted ball that goes directly to the catcher's hands and is legally caught by any fielder.

Who has seen this happen? bounces off the catcher's mitt and F3 catches it on the fly - 3rd strike on the batter and ball is live.