First, the case of a badly run business, that just doesn’t make enough money. Banks won’t lend you money so there will be nothing to pay back. Suppliers will tend not to deliver without immediate payment, again nothing to pay back. If you extracted money from the company, you may have to pay it back. In the UK, it is illegal to pay dividends if you then can’t pay your bills, so you’d have to repay them. Loans to the owner must be repaid. Taking money out of the till gets you into trouble and has to be repaid. Salary will likely be safe.
Now if something bad goes wrong: If the company causes damage that leads back directly to you, then you will be personally liable. Assume the company had two owners. If you make a bad decision the other owner might say that this wasn’t the company’s decision, but your personal decision.
Look at “breach of contract”. You have a removal company. Not removing furniture on the promised date could cost a lot of damages. If your removal truck breaks down, your company is liable. You are personally safe. If you find out the customer is the person who stole your girlfriend 30 years ago and stop the removal, that is also breach of contract, but you would be personally responsible.
With vicarious tort liability, we can assume that a company or company director wouldn’t commit a crime, but that a crime would be because of a personal decision if the owner. So the owner would be personally liable. (That’s also a situation where a second owner would insist that you pay damages personally, and not the company).