If one or several break off, just leave it, the tree will grow over it. However, if several break off either they were set too hard or you are pulling them incorrectly. The maple companies make a tool for the removal, but I made my own. I used the cheapest version of a Stanley Wonder Bar, when I got them I paid $1.89 at Big lots (several years ago). At that time a real wonder bar was well over $10. I then used a 1/2" sanding sleeve on a Dremel arbor, the type that grip the arbor by tightening a screw to expand a rubber sleeve, locking a sanding disc in place. Then I used it to grind a slot about 1/2" deep in the little V groove on the short end of the tool. It wore out a disc in about 1.5 slots, but I made 4 such bars to pull taps in about 10-12 minutes. To use it, just push the groove around the neck of the spout, behind any shape that is larger, and with the simple flick of the wrist the tap pops out. Some years maybe 2-3% loose the tip in the hole, leave it, most years that may happen on 1 or 2/1000 taps. If more than that the taps were set too hard. When installing a tap, use a light weight preferably plastic hammer (Or I use the flat side jaw of a 7" pair of lineman's pliers). Swing gently and listen, the sound will change to "thunk" when set. Don't hammer them in any more.
Dave Klish, I recently ordered a 2x6 wood fired evaporator from A&A Sheet Metal which I will be converting to oil fired
Now have solar, 2x6 finish pan, 5 bank 7x7 filter press, large water jacketed bottler, and tankless water heater.
Recently bought another Gingerich RO, this one was a 125, but a second membrane was added thus is a 250, like I had.
After running a 2x3, a 2x6, 3x8 tapping from 79 taps up to 1320 all woodfired, now I'm going to a 2x6 oil fired and a 200-425 taps.