All I can say is I've definitely seen bailiffs go to the person's home because they had a business debt but the writ was made out in the name of the individual rather than the business. So it must be possible although I don't know the inns and outs.
I think you should stop watching that awful game of thrones programme and watch channel 5 instead!
I watch that show B2R, and you're right in what you saw, but in a different way.
The bailiffs are following up a business debt, often at the home of the Director of the business...because that address is listed as the registered business address.
If the man pays up, (from his business account), then fine... but usually they can't or won't.
Then the bailiffs have the job of trying to seize assets, such as cars or computers that are part of the business asset.
The crooks are usually too clever for that, and the cars are in 'their wife's name' or suchlike, and can't be touched. It's a great show, a little frustrating sometimes.