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You may want to propagate the succulent with leaf cuttings to give your plant new life.
Here are links to help with this.

https://www.gardeningknowhow.com/houseplants/hpgen/propagating-your-houseplants-with-leaf-cuttings.htm
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/propagating-cacti-and-succulents.htm

You can remove the flower stalk as close to the main stem without damaging the plant.

Surely does look like spittlebugs work. Take a look at this article too: https://www.gardeningknowhow.com/plant-problems/pests/insects/spittlebug-control.htm

I'm not sure what kind of succulent you have, but this article might help:
https://www.gardeningknowhow.com/houseplants/jade-plant/limp-jade-plant-help.htm

Some succulents really need very little water. Even if it's not overwatered, your plant might need less water than usual in its weakened state. Water that it can't fully absorb might hurt the roots.

You should also check your plant for any visible insects on the leaves and stem.
This article is about cacti, but might help you identify the problem:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/cactus-going-soft.htm

I have had good luck moving a plant in a cardboard box that is as tall as the pot but shorter than the foliage. I packed newspaper in around the pot, then taped two sides of the box down to stabilize the pot. I taped the other two sides of the box up to protect the foliage.

Also make sure the temperature in the vehicle where the plant will be transported won't be freezing or broiling. If your move is going to take more that a day or two, so that you won't be able to care for the plant for a while, you could try the method of packaging plants for mailing described here:

https://www.gardeningknowhow.com/garden-how-to/shop/shipping-live-plants.htm

This is a Rosary Succulent or String Of Hearts.
https://www.gardeningknowhow.com/houseplants/rosary-vine/rosary-vines-indoors.htm