I used to work as an internal auditor for a debt company - didn't stick it long though, as it is obviously a horrible working environment.
Over here, not all debts are purchased - it's actually better if they are, because only a % of the original balance changes hands & the rest is written off, meaning the agency then in ownership can not charge interest etc & can afford to take a full & final settlement figure generally well below the initial debt size. Some co's don't pay commission, as such, to their staff, but staff are targeted and pressured to achieve, because the agency will be in competition with similar agencies for the percentage share of a client's debt.
There might be a case to legally withhold payment, where deb't been sold, as you have no contract with the 3rd party.
If you do pay a reduced settlement, the balance is written off, but it can still go against you, as the creditors notify credit reference agencies.
A lot of banks, telecoms co's & utility co's use agencies to collect on their behalf, and pay them a set percentage of collected revenues. Some of those bastards continue adding charges + interest, regardless of the customer's circumstances. And I could name one which will, despite cancelling your credit card, still continue to allow direct debits to be drawn against from it. They don't tell people this as a matter of course, so that leads to yet more debt, confusion & anger.
A part of my role was to listen into phone calls to ensure that the kind of scenario in the OP didn't happen, and instigate training and / or disciplinary procedures for any breaches in policy & DPA. Even from the brief time I was there, I could write a book. It would read like an Edgar Allen Po.
What I will say though, is the FSA have stepped in in recent years, to try to help stop harassment. Companies & individuals employing brow-beating tactics can be fined & lose their licence to trade (or be sacked). Also, any complaint you make to the financial ombudsman will automatically result in a charge of around £400 being incurred by the agency, regardless of whether the finding is in the claimant's favour or not.
You can advise these companies that they are only to communicate with you in writing, and they're obliged to comply. That slows things down too.
If they ring more than once in a day - say they leave a voice mail message, then try & catch you later the same day - that alone can be classed as harassment now.
They're not allowed to advise you to try to get a consolidation loan.
They're compelled to be civil and non-judgmental.
If you can't afford to pay off a balance, you should write in with your income & expense details and make an offer based on your disposable income. They aren't allowed to refuse it, although they may request proof of the details if they seem unreasonable.
Surprisingly, a lot of these companies & their staff don't seem to know these regulations. It's easy to catch them out, and a letter to them, pointing out how they've subjected you to harassment, and stating that you are now reporting them to the FSA & FO can sometimes magically make the debt disappear.
A lot of people in the UK fall prey also to various debt management leaches. NEVER use one. They calculate your disposable income, & make pro-rata offers on your behalf to all your creditors. They do not have any power to get interest stopped, or insist that creditors accept their proposals. They will keep your first months instalment for themselves, paying nothing off your debts. All subsequent payments will have an amount deducted as their fees - which would have been better used to clear the balances.
If anyone can't cope with doing those calculations for themselves, there are government run ones (believe it or not) who will do it for free! Though they're crumbling under the sheer numbers of people who are struggling.
And yes, debt collection agencies are arse-holes!