Bankruptcy is not a "get out of debt free" card. If Barb files Chapter 7, basically the foreclosure will be put on hold for a few weeks to months until the bank counterfiles and proceeds with sale of the property. If she files Chapter 13, she'll have to renegotiate the debt with the lender to pay it off in a set period of time (usually a few years) or the lender immediately seizes the property. Different states have different specific laws about primary residences, but that's the usual way of it.
Virginia has a very small homestead bankruptcy exemption, so they would lose the house in a bankruptcy.
Some states have much larger ones, so people with modest houses won't lose their home. States don't tie this to inflation though, so they have to keep increasing it to keep up. Virginia is one of those states that hasn't. The situation gets worse when property values spike, as legislators are lose to make massive increases to the exemption.
For instance in California the exemption is a seemingly-generous $300,000 in counties where the median home price is less than that, or whatever the median price is, up to $600,000. This means that in shithole counties almost nobody who actually have their life destroyed by bankruptcy loses their house that they have lived in for more than 3.5 years. In a middling inland place like Fresno, the majority of people are still safe.
But while this exemption is one of the higher ones in the country, California can be expensive. If granny lives in a coastal county she's fucked. The house she bought for $50,000 is now worth $2 million. Better hope she didn't get another mortgage like Barb did, because she's gonna have to move to Fresno.
In Virginia the exemption was recently raised from $5000 to $30,000 (by adding a wildcard $25k property exemption). It saves pretty much nobody. If Barb/Chris declares bankruptcy, they're fucked and are better off just selling the house and pocketing the equity.
In Texas the exemption is unlimited, so you never lose your house (provided you lived there for long enough). You also get to keep one car per driver. Lenders pay a bit more attention to ability to pay in Texas, and bankruptcy basically means you'll never get credit again.
Without a will, the total of the estate goes to a surviving spouse before children. Bob's prior children don't get a look in. That would be Barb. When Barb dies it will be split up between her heirs since Bob's estate is now her estate. that would be Cole and Chris.
Technically under 64.2-200 they were entitled to 2/3 of the property. We don't know what happened on Bob's death and if they chose not to take their share. Most likely they didn't even think about it. They might be able to sue to claim their share now due to the fact that Barb never bothered to transfer the title to her name and left it with the joint ownership. The statute of limitations for inheritance lawsuits in Virginia is one year, so Barb/Chris would be able to argue that since Bob's kids never claimed their share, it's too late to sue for it now.
EDIT: Also IMHO this law is pure bullshit. It's basically a race to see who dies first, and the kids of the first dead person get 2/3rds, and the kids of the other spouse get 1/3rd when the other spouse dies.