If you file for bankruptcy, your pending claim becomes part of your bankruptcy estate and your bankruptcy trustee takes over control of it. You will have no control over whether the case should be settled or for how much, or even whether the case will continue. It is a very expensive alternative, but it may be a better alternative than bankruptcy, to seek a pre-settlement advance. You should certainly discuss these matters with the lawyer handling your case before you do anything.
When you file for bankruptcy protection your unsecured creditors are entail to the value of your non exempt assets like the potential judgement you described. In short you will lose the assets if it ends up being worth anything.
You didn't tell us what this trial is about. If it is for a personal injury--like an injury from a car accident or medical malpractice--you can file bankruptcy and under Virginia law the personal injury claim would still belong to you. If it is for economic damage--like employment discrimination or just the damage to the car or like flood damage to your house--the bankruptcy court could take over some of it, maybe all.
Of course filing bankruptcy could have some affect on the timing of all this
To get a good answer, a lawyer really needs to know what this litigation is about. You already have lawyers who know what the litigation is about, so you should start with them. They could suggest bankruptcy lawyer there in Richmond to talk to if you need more information.
If you have a legal matter going on, it's usually not a good idea to be doing things without telling your lawyer.