I made a ton of jams and jellies about six weeks ago to sell at an upcoming open house. Normally I am very diligent in ensuring they have sealed within 24 hours of processing before I put them away. Unfortunately there was a lot going on so they got put aside in the jar boxes after they cooled and I forgot to check them to see if they sealed properly. I've never had jars not seal properly, so I probably didn't think too much about it. But this time I had seven jars not seal (out of about 100). Of course it's all different flavors, so I can't blame one fruit for being uncooperative! They haven't been opened since their water bath. Despite not sealing, are they safe for consumption? Can I reprocess them after that long (I know for marmalade you can up to about two weeks but none of these are marmalade)? Or should I just dump them all? I'd prefer not to waste them if possible. Of course I wouldn't sell these, but if they are still safe for me to eat...
The standard answer is that NO you cannot reprocess them and you should not eat them (and thus should toss them). These unsealed jars should be considered similarly to jam that had been placed into a plastic tupperware-type container and put on the counter for the same length of time.
If you would feel comfortable eating jam that had sat unsealed on the counter for that length of time in a tupperware, then I suppose you could eat them. Personally though that sounds gross to me (and my health is more important than 7 jars of jam).
Of note: Marmalade is really no different. It too should not technically be consumed/reprocessed more than 24 hours after the original processing unless it had been placed into the fridge. (Canning "rule-of-thumb" is that things can be reprocessed/eaten/refrigerated within 24 hours of the processing and considered safe.)
As they are jams, they are a high-acid product (assuming you followed canning guidelines and didn't try to jam once of the few low acid fruits like watermelon). This means that any spoilage is going to be mold or something similar so botulism shouldn't be a concern. Additionally they are unsealed so the "air-free" environment that botulism likes is not present.