I don't know the company laws or the Liquidation laws that prevailed in 1881-1882. Today anyone can set up a company without too many restrictions and red tape.
Liquidating a company doesn't have to be anything sinister.
A partner in a business might want to take his share of what the company is worth and use the money for something else (a ticket to a new country, for instance). I found that this was the case in the 1800's with a family I was following who had many fingers in many pies. When I saw the first liquidation notice I was shocked to think it might be bankruptcy but it was the family re-arranging their business interests; e.g. taking a share of money out of one partnership and setting up new partnerships.
When my OH and I started up our own business in 1972 we had to legally register that we intended to set up a business partnership (company) and go before an (expensive) actuary to swear to abide by the law (which cost us money) and we were allotted a Registration Number.
As there was just the two of us we each owned 50% of the business.
Four years later when the company grew we decided to change the type of company which meant we had to de-register (liquidate) that official partnership business. In order to "liquidate" we had to provide a list of the value of everything in the company (office equipment, stock, etc) and also make a list of creditors who owed us money and a list of debtors we owed money to.
As per the law the liquidation of our registered partnership business would be made publicly known in the press.
You'll laugh at this ... The liquidator also calculated how much salary we'd both taken from the company over those years ... remember the 50% share? ...well as I'd taken less wages than my OH my share of the cash at the end of the proceedings was much larger than my OH's
As that partnership company had not made a loss we had money to put into a new registered "Limited Liability" company.
If Eliza. mentioned in the 1882 liquidation case was the widow of Thos, then she may have done what I did when I became widowed. I had the company assets valued and decided I could sell off various assets, pay the creditors and not owe money to anyone. In other words I liquidated the company so that I could retire and the liquidation notice was publicised as the law requires.