sometimes, although the instructions and most people say not to. but my grandparents lived through the depression and they taught me how to jam, and as far as they were concerned you couldn't afford to waste it. so as quickly as possible pour it all back in the pot, add some more sweetener or pectin (not too much!) and reboil. repour. listen for the lids to pop (you do have to use new lids unfortunately, the seals only work one time.) if they don't pop right away, turn the jars over on their lids for 15 or 20 minutes and then turn them back right side up and they should pop. or if you don't want to take the chance, put them in a water bath once they are poured and lids on, and that should pop them. i just use the invert method myself.
not setting usually means either too much juice was in the mix, or not enough sweetener and pectin for the amount of fruit. if you make low sugar or low sweetener jellies and jams, they will never set solid but if you buy organic or low sugar jam it also isn't set. it just can't solidify without the sweetener. so if low sugar was your aim, they are fine as long as they sealed, but you will probably have to keep them in a freezer because the sugar is also the preservative. i make all my jams half-sugar and that's what i do with them. when i give them away to friends, i tell them to keep them frozen and once opened use within a few weeks.
if the reason your stuff didn't set was that it had too much juice, you can boil it down so there is less of it and it should set properly. i'm sure some people will tell you it's not safe to reboil your jelly, but honestly unless i was hoping to sell it i don't believe it is dangerous or bad to do. if selling, i would probably keep the unset or recast jelly for myself and start from scratch for selling, just because people are always looking for an excuse to sue you.
My first batch of strawberry jam did not have enough pectin...It was more like IHOP fruit syrup. Instead of wasting the lids, by opening them all up, when I get ready to use a jar, if I want a firmer jam, I just throw it in a pot and add a teaspoon of pectin, and keep adding, until I've got it like I want it.
It depends on what kind of jelly you made, I have certain recipes that take up to 2 weeks to firm up and others like strawberry which are usually set by the time it cools. It is perfectly safe to reboil and can the jelly again if necessary
Here are remake instructions for jams/jellies that the Extension offices handout. I used them once on mulberry jelly and it did work.
To remake with powdered pectin:
For each quart of jelly, mix 1/4 cup sugar, 1/2 cup
water, 2 tablespoons bottled lemon juice, and 4
teaspoons powdered pectin. Bring to boil while
stirring. Add jelly and bring to a rolling boil over
high heat, stirring constantly. Boil hard 1/2 minute.
Remove from heat, quickly skim foam off jelly,
and fill sterile jars, leaving 1/4-inch headspace.
Adjust new lids and process as half-pints or pints
for 10 minutes in a boiling-water canner.
ETA: and here are instruction using liquid pectin. I have not tried this one.
To remake with liquid pectin:
For each quart of jelly, measure 3/4 cup sugar, 2
tablespoons bottled lemon juice, and 2 tablespoons liquid pectin. Bring jelly only to boil over
high heat, while stirring. Remove from heat and
Quickly add the sugar, lemon juice, and pectin.
Bring to a full rolling boil, stirring constantly.
Boil hard for 1 minute. Quickly skim off foam and
fill sterile jars, leaving 1/4-inch headspace. Adjust
new lids and process as half pints or pints for 10
minutes in a boiling-water canner.