How do bankruptcy limits on property liquidation work?

Keeping 'up to' a certain amount of equity means that if your net assets are equal to or less than a certain amount, you won't need to sell them during bankruptcy proceedings.

So if you had a car worth 1k that you owned, and had no debt on it, you would have 1k of equity, so would not need to give it up.

You seem to be focusing on the 'fairness' of bankruptcy protection laws, and on that I will make two points:

(1) This site can't answer for any perceived unfairness in a particular jurisdictions laws. It might help to understand whether some people find a law fair or not, but that doesn't mean an answer explaining the law finds it fair.

(2) Bankruptcy protection laws exist to protect a human being at great risk of being destitute. There are many times when a just society will step in and provide benefits to someone who cannot support themselves, and that does not mean it is 'unfair'. It also doesn't mean that a law that attempts to protect someone will always work as originally intended.

You are implying that someone with more net assets benefits by being able to hold on to more assets - in the wording of what you have provided in the question, that is true to a point - someone with a $9k car can keep $9k in net assets after bankruptcy, but someone with a $1k car can keep 1k in net assets after bankruptcy.

You could say the second person should get an extra $8k 'bonus' somewhere for 'fairness', but that might be difficult to administrate, when the goal of the above would presumably be to allow someone with a car worth less than 10k net, to keep that car and continue to operate in society, such as continuing to go to work, go to school, go on errands, etc., and that general intended benefit may be seen as outweighing a perfect dollar for dollar 'fairness' outcome. [Someone with a car worth more, net, could more easily sell the car and use the proceeds to get something driveable, but someone with a car worth 1k might find it difficult to do likewise].