Why would anyone choose to file for bankruptcy?

A bankruptcy wipes out the debtor's resources to pay creditors.

This is a bit of an overstatement. Bankruptcy comes in many forms. For individuals, the most common for is "Chapter 7", in which most of your debts are forgiven in exchange for a liquidation of assets to pay part of what's owed. Secured loans (e.g. car loan) can be taken care of before bankruptcy by just surrendering the asset (repossession) and making up the difference.

A bankruptcy will require the borrower to liquidate enough assets to pay off the debt. One doesn't necessarily have to lose everything

If one has some paid off property but defaults on some unsecured accounts why would he or she want to file for bankruptcy thus risking liquidation of his/her assets?

A house is typically exempt from liquidation if the borrower is current on the mortgage and doesn't have a lot of equity. There is also a "homestead exemption" that varies by state that can be used to protect a house in bankruptcy. But, if one has, say, a million dollar paid-off property, they will possibly have to liquidate it to pay off unsecured debt. I would suspect that is very uncommon, though. More than likely someone declaring bankruptcy will have little to no equity in their home that is well under the homestead exemption.

What would be a rationale behind such a filing?

It is the last resort to recover from crushing debt. It stops debt collectors from coming after you, threatening to sue, and generally harassing you. It typically reduces the overall debt burden and gets rid of exorbitant interest and fees that may have piled up.

It can also prevent judgments from being filed on you by individual creditors, or remove existing judgments. A lawsuit would require you to show up in court (hopefully hire an attorney), and if a judgment is placed against you, the payments can be taken out of your paycheck (up to a certain amount depending on local laws).

It also put you back on the road to get back to credit recovery within a few years.

In addition to D Stanley's good answer on more common ways bankruptcy may occur and some of the protections it can provide, it is also possible that someone may simply have more debt than assets. If your debt is eligible for discharge on bankruptcy (notable exceptions would include some student loan debt depending on jurisdiction), then bankruptcy may immediately increase your net asset position from negative something to near zero. Not a good position to be in after declaring bankruptcy, but 'good' is a relative statement!

The answer is very simple,

why would he or she want to file for bankruptcy thus risking liquidation of his/her assets? ...

in many cases such folks have little or no assets.

So indeed, you're 100% correct that (in certain jurisdictions) if you, say, own a house, it would be insane to attempt bankruptcy, because it would be stripped from you. You're correct.

Note however that in many jurisdictions, if you go bankrupt you DO NOT have all assets stripped from you. So, that's the second answer to your question.