The reason you inherited a Basset Hound is because they’re hounds. They use their long ears while chasing to ‘scoop’ up scents for their nose to interpret.
Their job is to track, and they were bred to short legs to get them through the bushes and thickets.
Like Beagles, they will track whatever scent they waft, and will be gone, and those that find them on their property (fish guts, deer parts, dead squirrels) will call the vet # on their collar.
Adopt a runaway, expect to chase a runaway. And I love Bassets.
Good luck, with a tall strong fence.
We are on our third bassett, all great dogs with differing personalities, but all loves.
They do tend to be a little stubborn.
Keep food deep back on the counters- despite the little legs, it is amazing how far they can stretch their bodies like an accordian and reach items on the counter. I had just walked in from work one day when I heard the wife scream-and the dog blowing down the hall (they can run fast). He had stolen about a quarter lb piece of chicken, not cooked yet, off the butcher block. He ran it like a bat of hell under our bed- where he knows if he lies right in the center, we can’t reach him. Luckily the chicken was boneless. They smell everything food- my current guy can find the wrapped meat in a bag when we get back from the supermarket.
Take good care of their ears, and give a lot of bellyrubs.