This is why a fuel sender dies. (with pic)

I had the contact slider pull away, just a little bend and it was back on track. I also saw one whos contact was rotted off, probably empty for decades with moisture ingress. Could you solder than one back together?

Can that be soldered or repaired in any way, or replaced completely with a new unit???

If the wire fails I don't feel comfortable soldering them.
For what one costs it's worth changing out for a new one.

Here's how I go about putting a new one in.
I disconnect the old sender and hook the new one up to the wire and ground the hanging sender.
Then I check the gauge to make sure that when the sender float is all the way down, that the gauge is also.
Then I pull the old one and lightly install the new one with only the wire connected up.
I put a gallon of gas back in the tank and pull the sender to bend the float arm and test again until the gauge just barely moves off empty.
Now I put the sender back for the last time with the feed and return lines all hooked back up.

This way I know when the gauge hits empty I have about one gallon left.