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Wormholes don't quite behave like portals in the game.
When something drops into a wormhole with zero velocity, the apparent mass of the entry end increases by the mass of the object and the apparent mass of the exit end decreases by the mass of the object. At some point one of the ends should acquire negative mass. I'm not sure what that means: either it literally behaves as a negative mass object or this is an indication of the wormhole becoming unstable and collapsing.
Similarly, when something with momentum drops into a wormhole, the momentum is added to the apparent momentum of the entry end and subtracted from the apparent momentum of the exit end. The apparent masses change in a way that ensures energy conservation. This means that the gain in energy of the "cycling" object comes from wormhole mass loss and transfer of mass from the high end to the low end. Again, if it's true that the wormhole becomes unstable when its mass is supposed to go negative, that would be the end of the process.
If you already postulate having enough negative energy to create a wormhole, there is no extra issues due to one of the throats having negative mass, except the weird acceleration effect, as I mentioned in my other reply.