Can someone get a property from my mother as compensation for the car accident if her properties are not wholly hers?

They could get her portion of her assets.

If she has auto insurance, i would not worry about it. If she does not have auto insurance, then with the exception of her house, they could force a sale of her assets, and take possession of the portion that does belong to her.

If your mother is solely @ fault for the collision, it is usually only her assets that can be used to satisfy and Judgment. However, there is an Owner Liability Statute in Mi. that also makes the owner of a permissively operated vehicle also liable. So you would have to sort out the "players" to know if there are assets that are in the driver/owner's name only that may theoretically become available to satisfy and Judgment. Of course, if there is auto insurance on the vehicle it will respond to any claims/suit by hiring a lawyer for you and by paying any valid damages up to the policy limits. It is, at least in my experience, rarely the case that an injured person/their lawyer seeks the personal assets of someone over and above the policy limits (unless liability is egregious, limits are very low and the at fault person has significant assets, etc.).

First, your mom should have insurance to take care of damages. If she does not yes they can get to whatever she owns or whatever interest she owns, subject to certain exceptions. See a lawyer if this seems imminent this is why people buy insurance.

If one holds property jointly with another person who is not their spouse in Missouri, the property may be attached by a creditor.

First, there are exemptions to what property can be attached and sold to satisfy a judgment. At this time, I believe that up to $50.000.00 in your home is exempt from execution to satisfy a judgment (if the property is not her home, then this exemption would not apply). I do not know the amount that you can own in a car that is exempt, but there is an exemption for cars. Only her interest in property that is co-owned is subject to execution on a judgment. For example, if she co-owns a car worth $10,000.00, then the car would be subject to execution only up to $5,000.00, which may be below the exemption. Same thing with real estate. In theory, I suppose the court could order that a car or real estate be sold to satisfy the judgment, and apply to the judgment only that percentage of the sales proceeds as the percentage ownership your mother has in the property. Most cases settle within the insurance policy limits, and there are a number of hoops that the Plaintiff must go through before it gets as far as selling property.