A hive lost?

The new hive in my back yard was not very active so I wasn't too surprised when I opened it up and found the hive nearly empty. Further investigation revealed a queen and about 50 workers alive and little to no brood. There wasn't any sign of disease but I set aside some comb that had scattered capped worker brood for further investigation.

My diagnosis is that the hive was robbed of all of its honey and with the cool weather the bees couldn't bring in enough nectar to keep the hive going. Furthermore the stronger hives in the yard continued to pester the weak hive. There were a few spiders and a few wax moths in the hive but the comb was still in good shape which means the hive crashed sometime in the past month.

I should have reduced the entrance size when the weather got cold and the activity slowed, the large entrance allowed the stronger hives to overcome the defenders and steal the honey. My decision now is do I let this queen and her small cluster of workers die or do I try and save them? I know the answer is that I should let them die but I am curious what would happen if I gave them some honey and protected the hive from further robbing. I put in a division board feeder and closed up the entrance to only a single bee width entrance and put the hive back in the yard. Once I did this the outside of the hive was covered in bees, a few of them nasanoving but most just trying to get into the hive where the top entrance used to be. After a day this activity ceased (the weather also turned cold). I plan to check on this hive in a few days to see how many bees are left alive in the box and to check if they have taken in the feed.

Even if the queen survives until the Spring I know that this hive won't produce much next year, they'll continue to be a weak hive. At this point I've got nothing to lose with the hive (other than the honey I put into it) so I'll learn what I can from this failure.