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i hope you're able to see the link above. Back issues in dogs (and humans) are usually the result of a herniated disc or discs. The middle part (nucleus pulposus) leaks out and can press on the nerves around it. Depending on where in the spine this occurs (if lower back-- more likely to affect the legs, and when severe, also bowels/bladder; if upper back or neck-- more likely to affect the arms, but can also affect the legs, too).
Yes, definitely can recur, but you will also hear stories of some dogs who only have 1 episode. My wiener dog was one. He had it once because he jumped up and down all the time from furniture and was overweight by 2-3 lbs (a lot for dogs) and stocky. when we made modifications, like having him lose weight and making ramps for him to keep him from jumping, it never came back again. his case was pretty mild.
Severe cases can require surgery which may or may not correct the issue (i think it helps more often than it doesn't help, but depends on individual dog). severe cases can also result in paralysis. severe = spinal cord compression, which sometimes can be permanent. If the problem is in lower spine, a dog can end up not being able to use legs well or at all (paraplegia-- wheels can help w/this, if you've seen dogs w/their hind legs on wheels). If the problems is in the upper spine or neck, a dog can become quadriplegic, not being able to use arms or legs. I'm guessing these are probably then put to sleep.
Anyways, those are the ends of the spectrum, and there are lots of conditions in between. Here on the forum, lots of bassets have done ok w/out surgery, just a lot of rest and pain meds and anti-inflammatory meds.
I included the link to the picture above to show that there are different stages of this. If the dog was taken to the vet, it might be useful to talk to that vet, and see what the severity was. Sometimes they can see how severe the nerve impingement was on the x-ray. That might be able to guide you a bit as to whether the condition is more on the mild side or more on the severe side. If more on the severe side, you would not want to take this dog on unless you are able and willing to pay for medical care, including possibly surgery, if needed, thinking practically.
if you do take him, probably one of the most important things is to put him on a diet. if he has back problems, he should probably especially be kept on the low side of normal re: weight, to lower the strain on his back. That is probably the first most important thing, even before exercise. Exercising an overweight dog can risk injury to the joints/back. that's why in a dog like him, prob better to have him diet first w/mild activity, then later when he is at lower body weight, to increase his activity to moderate level, if he can tolerate without injury to his back.
Please keep us posted, and if it works out, post some pics! Good luck with your decision!