I guess technically we can’t sell an IRS as it’s not a product like an orange (or a house, or an option) with an owner. A IRS is a long-term bilateral agreement. Analog? I can’t “sell” my insurance policy to someone else.
A liquid swap market lets us offset our Libor exposure —
Suppose I’m a Payer in Deal 1 with Citi, to receive Libor and pay fixed 4.5%. Five hours (or 5 days or 5 months) later, I could become a Receiver in a JPM deal (Deal 2) to pay Libor and receive fixed 4.6%. Therefore I get rid of my Libor exposure, as long as the reset dates are identical between Deal 1 and Deal 2. But strictly speaking I haven’t Sold an existing swap. Both are long-term commitments that could in theory be unwound (painful) but never “sold” IMO.
By market convention, the counterparty paying the fixed rate is called the “payer” (while receiving the floating rate), and the counterparty receiving the fixed rate is called the “receiver” (while paying the floating rate).