small fish eating large one

For the last several years I had two GF in a 50 gallon tank -- both
were feeders I bought
when they were small, and both grew to a nice size. One had the most
beautiful fins,
white and long and lacy. Recently the other fish died and I replaced
it with another
small feeder. Of course my fear was that the large fish would eat the
small one, but
the small fish hid in the plants for several days, eventually getting
large enough
or confident enough to swim around freely.

Now I see to my dismay that the small fish is eating up the fins of
the big one. I hate
the idea of disposing of the small fish and I hate the idea of letting
nature take its
course and I don't really have the room to set up a whole new tank so
I can separate
the fish. But those are my options, I guess. Any suggestions??

Let me add some more history, just to see if it sparks a response.

Like I say, I kept these two GF, both on the order of 7-8" in a 50
gallon tank. I swap out 5 gallons a day, every day. My filter isn't
much, but I figure
given I am adding clean water at a pretty fair rate I don't need the
best in the crowd.

About a year out of nowhere I started getting some kind of growth in
the tank. It's like a brown algae, which I guess means it might be a
fungus, though in fact I think I have read that there are brown algae
-- they carry enough brown pigment to overpower the chlorophyll.
That's what it looks like, but it doesn't seem like the fish are
eating it. After a year or so one of the big fish died. Perhaps there
was a connection -- I think the GF fish were about ten years old,
which might be getting on for a GF or it might be the first blush oif
adolescence, I dunno. After the first fish died I noticed that the
second started to look "old" -- slow and lethargic and quiet. It sits
on the bottom of the tank a lot doing nothing, which it didn't use to
do. Perhaps it is getting old or perhaps the brown algae killed the
first fish and is now burdening the survivor. On the other hand the
feeder fish I just got, the fin eater, could
not have been livelier.

Any of this ring a bell with anyone??