How typical is it for old people to fall in depression when their partner gets seriously ill?

Yes: Yes it is. Your partner has become a big part of your life and your identity. When your loved one can no longer participate in the things you once shared - that is a loss. When you see a loved one in pain - you grieve. When you think about possibly losing your loved one - you fear. Make sure to spend time with others who care for you and can provide comfort. Prayer may also help. Take care.