In most cases, the calf will nurse the quarter. The next alternative is to milk out the quarter by hand. If it is too bad, sometimes the quarter will be lost. Udder and teat structure of cows for the cow/calf producer is important as, in most cases, producers don't have the time or facilities to milk a cow out on a daily basis, which is necessary if the calf does not nurse the quarter.
As an aside, poor teat and udder structure is partially controlled by genetics and can be included in a replacement heifer selection criteria. In other words, you would consider not keeping a heifer as a replacement if her mother had poor teat and udder structure.