Everybody I knew went in under a tourist visa and then just overstayed it. A few people renewed it, but you def don’t have to leave the country to do so–you just go down to the misrad hapnim.
When you leave, they yell at you for not renewing it, and sometimes write nasty and scary things on your passport. But you just tell them that the misrad hapnim was on strike (it isn’t lying, because it really was–you can look it up and check yourself). I didn’t check, so I just said nothing, and then came back and did it again.