I had a old Kohler starter awhile back that used a Bendix similar to what you describe and bsengine indicated some of the Tecumseh"s used the same Bendix slip clutch type as you describe when I asked questions about mine on this site. I had never encountered the rubber clutch type Bendix type. The rubber slip clutch kinda gives the starter gear a soft start spin when it first meshs into the flywheel which prolongs tooth life of flywheel and Bendix gear. They made couple mods to the new style Kohler kit that prolongs the clutch life as compared to the old style and if you get the kit you may see few extra parts that are not used or needed on some of the starter end shaft designs. (Make sure you install the new kit in proper order, springs washers, keepers, etc.
I bought a complete Kohler replacement starter from flea bay for like $38 with free shipping, then after I took my old starter completely apart to see if it was worth repairing, checking brushes, bushings and the start torque and amps I seen that the old starter only needed the new style Bendix which costs about $12, so I repaired my old starter as a spare. The starter on this Kohler engine was in a very hard place to access and I wanted to make sure I installed a real good starter in one shot is another reason I went with new replacement. It was own my own eq. counting time spent checking the old starter and searching for parts and repairing the old starter (making sure I was not whipping on a dead horse, the old starter) I now have about $200 in time spent for repairing and saving the old spare starter, but I have a good spare.
If you give complete engine model info someone on here maybe can guide you to a kit, assuming your old starter is ok or talk to these people that sell starters and parts on flea bay.
I've bought small engine starters (mostly Briggs) and starter parts from these guys (dbelectric) and everything has worked out great with fast shipping with tracking provided in the USA.
Here is who I get my starter and parts from dbelectric on Flea bay and I've had real good luck with their replacement starters and parts.
dbelectrical
and a link and a Tecumseh starter
example only so as you can contact them about your starter questions.
130598100346
http://www.ebay.com/itm/New-Starter-Tec ... 1e6840dd7aSome of them old square type Tecumseh starters are in the $80 area and if yours is in this category you might want to give yours a good exam before ordering any parts to make sure you are not whipping on a dead horse.
and to answer your other question, on some small engine starters the Bendix gear will stay engaged in the flywheel if the engine don't start or the flywheel don't spin fast enough to run the gear back when the starter voltage is removed while cranking.