The news comes as it emerged that Lloyd's is to enter discussions with an American names association to try and strike a deal with US names who have so far not met their underwriting liabilities to the market.
Until now it has been a closely guarded secret that the new debt collectors were offering some names a capped deal.
Philip Holden, head of Lloyd's Financial Recovery Department, said it was possible for names to negotiate a cap to their liabilities to Lloyd's. He added that it was all dependent on the names' assets and liabilities.
Mr Holden said: "I am not keen on litigation. I am keen on a negotiated resolution. For that I need names' agreement."
Mr Holden added that this "demonstrates Lloyd's willingness to deal sensibly and sensitively with the problems of its members".
However, names are suggesting that recent court developments have forced Lloyd's debt collectors to disclose that a limit to their liability can be negotiated by some names.
In November the Appeal Court ruled that there must be a full hearing of names' claims that the arrangements at Lloyd's contravened European competition law. There will also be a separate hearing brought by names in the UK court where more names are alleging fraud.
Names claim that if these cases go their way they will not have to pay their losses to Lloyd's. Until these cases have been resolved Lloyd's cannot pursue non-paying names through the courts. The cases could take many years to resolve.
The US names have refused to pay their liabilities because they too say they are the victims of fraud by Lloyd's. Talks are to be held to resolve a lawsuit that US names have brought in California, which seeks to release them from any obligation to pay Lloyd's.
If there is no out-of-court settlement the case will go ahead and the names will get discovery of what they claim are sensitive Lloyd's documents which, they say, will prove their fraud allegations.
A US name commented: "They are coming over here to settle our lawsuit. They find it so scary they don't want it to go to court."
Lloyd's is planning further talks in March with individual US names to try and negotiate a settlement.
UK names are concerned that Lloyd's deals with US names will be on more favourable terms. Christopher Stockwell, a leading names activist, said: "Names cannot be pursued through the courts, so of course Mr Holden needs names' agreement. But any name would be silly to pay Lloyd's until the fraud cases have been resolved."Reuse content