Mine are purely indoor rabbits, though when I lived in a house with a fenced in yard I VERY THROUGHLY rabbit proofed the fence and brought them out occasionally. The trick with closing gaps at the bottom of a fence is to have chicken wire going down, but instead of stopping when it reaches the ground (they can always dig under that), about half a foot of excess should bend into a corner and lay flat on the ground. Rabbits trying to dig under the fence don’t realize that they need to dig half a food back from the fence, rather right at the edge of the fence. And the grass will quickly grow through the wire and nicely hide it.
But I personally am always paranoid of what might happen if my bunnies get away from me while outside. I take Delilah out a lot, because she LOVES meeting people, and Lahi goes out too to the vet and such. What if something happens? How will they be returned to me if they somehow get away? Lahi hates being touched and will run from anyone who looks like they might pick him up, and Delilah loves to be pet but is scared of being lifted, and will run from hands if she’s not in a petting mood. In the hypothetical situation that they’re outside and have gotten away from me, they’re probably scared and even if I’m around won’t neccessarily come toward me. To a certain extent I’ve trained Lahi to see me as a way to get out of a strange and scary situation, he’ll come over to me and reach up to put his paws on me, but that’s no guarantee.
So: before they leave the house, always, they both have y-front harnesses with tags attached that have their names as well as my phone number, same as dogs would. Even when I was just letting them run around in the backyard, they’d have their harnesses on. The tags made some noise that helped me keep track of where they were, and if I needed to grab them in a hurry the harnesses made that easier. If they ever got out, anyone else who found them had a way of returning them to me.
Delilah, who goes out more than Lahi, and doesn’t stay in a carrier when she does, is also microchipped. Tbh the chances of anyone thinking to check a rabbit for a microchip are low, but there is a chance, and therefore I have done it. I once had someone come into the clinic I was working at with a black lab that had no collar, and asked me to check for a microchip. There was none. That dog probably never made it home.
When I bring Delilah out in her stroller to meet people, I also have a leash clipped to her harness as a “safety belt”. She’s never jumped out of the stroller, but in the event that one day she does, I have a way to catch her that doesn’t require me to actually get my hands on her first when she’s potentially scared, in pain, and trying to hide.
In terms of finding rabbits escaped outside... I have seen once, a little cream bunny sitting out in a bush by a sidewalk. He wasn’t scared but when I got too close he hopped away. He’d begun living in a small wooded area behind some houses. I knocked on the door of the house he was in front of and the lady said that she’d seen him around for the past few months, and had been leaving carrots out for him, which was why he was so fond of that bush. She hadn’t known that that cream colour meant he wasn’t a wild rabbit. Based on what I saw of him, and the fact she said there were more, either someone had dumped a bunch of really young baby rabbits, or a pregnant mom who subsequently gave birth. I helped the lady set up a live trap for him and put her in contact with the local rabbit rescue, who wanted to come out and catch the bunnies, but I never heard what happened. Either way... these bunnies had been living outside long enough that there was no catching them by hand.