Copy files from a failing drive

A fried of mine gave me her laptop because it was behaving wierdly. This was (Still is) a hard drive failure, and I suggested her to backup her files before installing a new hard drive. I booted the computer with Ubuntu on a flash drive to backup her files (Mainly family picture and movies), but I still struggle to copy the files : when a file is corrupted, the copy function waits for the copy to complete. Is there a way I can tell the cp function to skip damaged files ? (Maybe telling it to skip files when the copy speed is too low) If it isn't possible, can you suggest me a tool which may be useful in that peculiar case ? Thanks in advance.