We usually carry spares. Tires that is. We hope they always remain spares and that we never have to use them. However, there's always the chance you have no spare or already damaged one tire, and now have a tire that's jumped off its wheel bead. It's rapidly lost all air and you have to find a way to get it reseated on the wheel and re-inflated.
If you stick to running street pressures in the dirt, it's highly unlikely you'll push a tire off the wheel bead. But airing down is an off-road necessity in many cases and without beadlocks there is some risk of popping a tire bead. When bead retention fails it almost always occurs on the outside wheel bead and very often on the downhill side of the vehicle where the weight of the vehicle is pressing the hardest on the tire sidewall. Other times, when bouncing laterally in deep ruts, a tire can be slammed sideways hard enough to blow the tire off the wheel bead.
A tire that's been knocked off the outer wheel bead can often be reseated, re-inflated, and then you can be on your way again. If the tire has come unseated from both the inner and outer wheel beads, you've got a bit more work on your hands to get both sides sealed again. In this situation, a large ratchet strap tightened around the middle circumference of the tire may help get the tire beads pushed outward a bit for a better chance of seating. Wider wheels also make reseating more challenging.
Getting the tire completely back on the wheel and re-inflated requires cleaning the bead surfaces on the tire and wheel, getting them pulled together, and getting sufficient air inside to inflate and seal the tire back on the wheel. It can be done in the boonies with a little technique and a good shot of air.
The first thing you must do is get the tire fully off the ground and high enough so it has room to be inflated without touching the ground. Short of this, there's no way to get the tire pulled back out towards the wheel bead for reseating. In most cases, it's easier to work with the wheel on the vehicle, using the rig as a solid anchor to hold it while you pull on the tire.
When the tire popped off the wheel, there's a good chance dirt or mud got inside it. We're not overly concerned with what got all the way inside, but we do care about debris on the tire and wheel bead areas. Always clean these surfaces before attempting to reseat the tire as debris here can keep the tire from fully sealing and holding air well. Feel free to wash down the bead areas with water which will clean and help the tire slide back on the wheel easier.
The final step of getting the tire back to a serviceable condition is to inflate it. If the backside bead is still in place on the wheel, that's a huge plus. In many cases, a couple pairs of hands pulling the tire towards the outside can get the outer tire bead out where it can start to seal again. Shoot the valve stem with air to attempt to inflate. You'll hear air hissing in locations that are not sealing. Shift your pull to try to get those spots to seal. Once the seal begins, further inflation will cause the tire to pop rapidly back onto the bead seat.
A voluminous shot of air helps greatly when trying to reseat a tire. A CO2 tank, or large air pump with reservoir, works best to get air rapidly back into the tire while trying to get the bead to reseat. A small pump often has trouble getting sufficient airflow into the tire to seat it. We've seen the starter fluid trick help reseat tire beads effectively. It involves shooting a few squirts of starter fluid inside the carcass, then tossing in a match to ignite the flammable material. Once the tire expands onto the wheel from the heated gases, one has to get to the valve stem quickly to get air into the tire for inflation. Often removing the valve core helps get the air inside quicker, but be cautious of hot gases coming back out of the stem.