Their motives are simple: Essentially the Agency is trying to get you to renew the limitation period by acknowledging that debt. Even if they can't get a payment now, there's always the prospect of recovery at a much later date with additional accumulated interest.
Thus, it's best to keep all correspondence to the telephone. If one has to reply in writing, it's preferable to indicate that you disavow ownership of the debt to legally protect yourself. Later on, for moral reasons, you can negotiate a settlement for 5% or 10% should you decide and be able to.