Yes you can sue an airline if it crashes and injures you or kills a family member etc.
To sue an airline for an airplane crash you would need to hire an aviation lawyer who deals in airline crashes.
It can be hard to sue an airline for an airplane crash and win though but it can be done and some people have sued an airline for the airplane crash and won.
The airline has to maintain the airplanes and failure to do so could cause a crash and if the airline did not have the airplane maintained properly and it crashed because of not being maintained or something failed on the airplane then you could likely sue and win.
But sometimes the airplane crashing is out of the airlines control or the pilots control due to something going wrong with the plane or something in the sky causing it to crash etc.
It's rare that airplanes crash and most airplanes fly through the air without any problems.
I've been on about 200 airplane flights and every one of those went really good.