I agree, adding sugar sounds like a bad idea. If there are some bugs in there you will be in danger!
I had a heather ale once go sour on me. Must have been some wild yeast and or lacto bacteria one the dried heather I added to the fermenter. I kept that sucker for a long time unsure what to do with it. Even attempted to dump it a couple of times but I changed my mind. I was not sure I enjoyed the flavor at first. It grew on me though as it got more sour. I enventually bottled what was left from the keg. Just a plastic tube (piece of racking cane) and stopper like I always use. I now only have 2 bottles left and I am reluctant to drink them as I will be sad when they are gone!
I guess the question comes down to how objectionable the off flavor is to you. Does it have some merit or is it totally nasty? If it has no redeeming qualities after all this time it likely won't improve with age. Can you describe the "bug character"? How does it taste? Is it like anything you have tasted before?
In the beer I mentioned above it had a strange pineapple flavor at first. As it got more sour I could still pick that out, but it melded with other sour fruit flavors and it dried out.
...Oh, and let us not perpetuate the stereotype that if a beer goes bad you should call it a Belgian. If it sucks, it sucks. Belgian beers do not suck, they are very deliberate.