It is often said that our fingers are not made to withstand the forces put on them during hard climbing. I seem to collect pulley strains at a decreasing rate of one per year or so. Early on this was from crimping all the time. Now I have rules for myself of when I can crimp, but the forces of the universe conspire against me. This time it started while trying the bottom of Parallel Universe at Rumney in the rain. If you've ever tried the route you already know on which hand the finger is, as well and the offending hold. Luckily I was able to keep it under control for a good spring send, but now I'm looking out at beautiful climbing conditions getting myself ready for a hangboard session in my dark, wet basement.
There is good discussion of finger injuries on the web here and here. I won't go deeply into how I treat my injuries, other than saying I try everything: contrast baths, cold water, heat pad, stretching, putty, etc. The training described here is probably safe if you have a slight pulley injury, I can't speak for other injuries: collateral ligament, flexor tendon etc.
Okay, now down to business. If you're going to train with an injury get used to the open handed grip.
My experience is that with a minor pulley injury one can pull as hard as you want as long as they don't close your hand more than the above picture. This is difficult, but not impossible, if you are climbing outside. The best tools, in order, are the fingerboard, campus board, and a bouldering wall where special problems can be set.
1. Fingerboard: Review the hangboard workouts on the workouts page of this blog. Notice that only one set of each workout asks for a 1/2 crimp hang. Either skip this hang or hang 3 finger open hand with the hand of the injured finger.
2. Campus Board: This is where I lose most people. The campus board is thought to be a very dangerous training tool. This is not deserved unless you campus with a full crimp. With an injured pulley one can safely perform any campus workout if they stick to a 3 finger open hang grip. This requires a fairly large degree of strength so its probably not best for everyone. I have even experimented with two finger open handed campusing during an injury without aggravating my finger.
3. Bouldering Wall: This requires problems to be set so that the hold for the injured hand can be grabbed 3 finger open handed(see a trend?). These problem can still be quite difficult, but care must be used to not close ones hand if the holds are poor.
Why is 3 finger open hand important? This grip allows the fingers to be loaded while remaining nearly fully extended, thus there is very little load on the pulleys. What about 4 finger open hand? In order to engage your pinky the other fingers must bend. This puts a nontrivial strain on the tendon pulleys. The 4 finger open hand/ half crimp is very safe for training on non-injured fingers, but not so great for an injured finger.