I knicked my nail on the sharp blade of a power tool. Later, it started to tear. If the tear is not too far into the nail bed, I will just rip it off and keep going.
However, this was going to go too deep. When that has happened in the past, my work has been hindered by the need to protect the exposed nail bed. It's been through trial and error that I have found a way to keep the nail intact and allow it to grow out until the torn section can be trimmed off. This method has been working very well for me for a few years now so I thought I'd share it.
I superglue the nail tear from the top and run a couple of lines of glue under the nail to secure it to my skin. The ends of my fingers get bumped a lot over the course of a day which will make the torn nail flex and the repair weaken. That extra bit under the nail really makes a difference in adding stability and durability.
Next, I trim down a piece of waterproof first-aid tape to fit over the tear. Then, I cover that with a thin layer of superglue. I repeat that a few times until I get a nice thick layer. This holds up very well for me no matter if I am working with abrasive materials or using chemicals. I can have my hands in water for hours, and the repair stays strong. I check it once a day and see if I need to apply a few more layers of glue.