Weird problem with starter today. Opinons welcomed!

Is this a mini starter? or
a factory Chrysler starter?

Cuz if it's a factory starter, I have rebuilt about a dozen of those in my lifetime. With this starter, the apron-mounted relay kicks in the solenoid that is mounted in the starter housing, which drives "the bendex" into the ring gear. This action closes a contactor inside the solenoid, which then spins the starter motor.
As long as the Bendex is in the engaged position, the starter will continue to spin, because she gets her power from a separate cable!
That Bendex is on clutch, so as soon as the ringgear is spinning faster than the Bendex is, the Bendex is just along for the ride.

This tells me that, if your starter is an old-style Chrysler starter, it is functioning just fine electrically speaking, but the Bendex shaft is probably dirty preventing it from retracting. To clean it, the starter will have to come down.
Or, it is also possible that the contactor disc is damaged, broken, or has welded contacts.
But my money is on, that the solenoid plunger has stuck in the engaged position, or the spring behind it has somehow failed. If you take it apart, do NOT grease it up, lol! That's just looking to do it over; as the grease gets cold it will get thick and the little spring may not have the power to retract it. Leave it dry.
Or it could just be sand, gravel, or just plain rust on the bendex axle-shaft..
Here is a CROSS-SECTION; sorry it's so small.....

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His bendix is fine. It was retracted because the relay was sending power to the starter. That's how they work. Starter starts spinning, the bendix kicks out. His starter simply stayed running, so the bendix stayed engaged, AS DESIGNED.