These days they prefer to be known as 'career management' consultancies and being part of the redundancy process itself gives them a crucial opportunity to build a relationship with the client firm.
Philip Beddows, a director at BG Careers, which is merging to become part of the recruitment and change management firm Whitehead Mann, says: 'We've always tried to make sure we're in the loop very early in the planning stage (of redundancies).'
'An HR director said recently that having us around had made a huge impact on those who remained.'
Outplacement firms get involved early on to advise their corporate clients on how best to manage the tricky process of making people redundant. They also provide a useful buffer between the potentially angry individual, and the employer.
Penna Meridian, which focuses on the financial services market, gets its message across using a quote from Valerie Gordon-Walker, the head of HR at UK West LB, on its website. 'Penna Meridian is an excellent supplier. I can trust them. Using their service allows us to remain neutral in difficult circumstances,' it says.
Alongside handling the messy job of firing people, outplacement consultants say that being on-site to meet people as early as possible is crucial to the success of their hunt for new employment.
'The way they manage that first day or two can have a huge impact on the next few months,' says Beddows.
Individuals are advised on everything from how to tell their families and their colleagues, to the importance of keeping their business cards, which give them a sense of identity and allow them to make use of their relationship with the firm. They are encouraged to look forward rather than back, and as a result to avoid litigation.
Once they have physically departed from the premises, they are offered a period of time - usually three months - to make use of office facilities, counselling and coaching.
Penna Meridian, for example, offers workshops that cover subjects ranging from body language to financial planning, image consulting, presentation skills and self-marketing by telephone. Its City office offers remote access to research facilities, career management software and online skills and values analysis.
Outplacement firms consider offering access to new technology to be essential for the research to gain a new job.
The average person made redundant in financial services nowadays is likely to be aged 32, technology-savvy and to have moved jobs several times. Many, of course, are female.
This is in stark contrast to 10 years ago, when they were almost certainly male, with an average age of 40 and had been with the same investment bank since they graduated from university.
Richard Chiumento, a co-founder of Chiumento Consulting, says: 'We find that in times of economic difficulty, cash is restricted and people are given less (outplacement) help. The younger person today is IT-literate and more familiar with job insecurity'.
One of the smaller human resources boutiques that also works in the financial services market, Chiumento offers a net-based virtual resource centre with more than 100,000 job vacancies across industries.
A peek at Penna Meridian's optional online job centre also reveals many big names in investment banking, such as former directors and heads of strategic planning at Deutsche Bank, CSFB, Morgan Stanley and ING Barings and others. They list their details anonymously.
But alongside online research, the importance of getting out and meeting people in the search for a job cannot be overestimated, consultants say.
Mark Allsup, chairman of Fairplace Consulting, says: 'We've always felt that the networking approach is effective - and in this environment it is still the best way of getting a job.'
In difficult markets, a key role of the outplacement agency is also to provide consultants who can give realistic advice.
'People often don't think rationally when they have just lost their job. They go through a fantasy stage and rush around contacting headhunters, expecting it to take a week or two. They talk about guarantees before they have been offered a position. It's important to manage expectations,' says Beddows.
Managing expectations is about getting to know the individual, and helping them discover what they want to do next.
Some outplacement consultants hold strong views about their role as counsellors interested in the person, as opposed to headhunters, who are seen as transaction-oriented, finding people for jobs.
'We are here to facilitate (the individual's) own search,' says Tom Kollinsky, who recently joined BG Careers from Meridian Consulting, now renamed Penna Meridian.
'We focus on getting them to take a step backwards and take a long hard look at themselves - their strengths, skill-sets, and weaknesses. It is about facilitating clear and personal change, which brings up all sorts of issues,' he says.
Penna Meridian has increased the number of its associate consultants from 40 to 80 in just over four weeks, a move its rivals have criticised as diluting the quality of service by hiring people who may have insufficient experience.
But the outplacement firm is fortunate to be able to draw on its wider business, which includes an executive search arm and a change consulting business as well as the increasingly in demand service of executive development and coaching.
Michael Moran, executive director of Penna Meridian, said last month that it made sense for underemployed headhunters to use their skills in outplacement.
It is a comment that has stung other outplacement firms working within financial services who say the skills are not easily transferable.
Squeezed by their clients' increasing attention to cost, some outplacement firms also complain bitterly of a trend towards bargain-hunting, saying it makes it that much harder for them to provide a decent service.
Linda Jackson, business director of the City office of Penna Meridian, says: 'It is a question of economies of scale. Meridian, as part of the larger Penna Group, has access to 600 consultants and we can move quickly if we need to. We can then afford to pass those economies of scale to our clients.'