If the date of last activity on the account was, in fact, June of 2010, they still could start legal action. Nonetheless, given the modest amount, the fact you're unemployed, and that they haven't done so yet means they likely won't. When they find out you have a job, to which wages could be atttached, that could change.
Anyhow, the CCP (Code of Civil Procedures) gives them 3 years from the default date to start legal action - unless you subsequently make a payment or provide a signed acknowledgement of the debt. So check to ensure that June, 2010 was the date of your last payment. Equifax simply lists whatever date the collection agency tells them to put down. Often, agencies manipulate dates as an enforcement tactic. Saving old account statements and correspondence from the creditor as the account goes into arrears is often critical for proving when the default date occurred. If you still have them, put them in a safe place.
No matter, whether you settle or not, the delinquent item will be on you Equifax and TransUnion credit reports for 6 years from the date of original default (or 7 years from the judgment date if they successfully sue you, in Quebec.) However, it will be marked as "settled" as opposed to being outstanding.
Because little further damage to your credit score can be done that hasn't already occurred over this debt, I would start by offering 35% of the current balance. I have no idea what they'll take, but often 50% can be obtained with little effort, Given the age of the debt and your financial situation, they may be amenable to less.
But keep in mind, the collection agency will likely try to trick you into agreeing to a settlement amount over the phone and then demanding further amounts later. If you had sent them the $2000 earlier on, you probably would have gotten stiff demands for remainder with more interest soon after.
Only negotiate over the telephone; if you mail a written setttlement offer, you'll likely needlessly renew the limitation period. Instead, bargain over the phone; then get them to send a written settlement offer (signed by a manager) indicating the offer is in full and final settlement of the account. Do this also if the agreement involves monthly payments, and demand no further interest accumulation.
Pay for Delete is illegal, and your chances of obtaining it with any collection agency is about zero. Not that the agencies have any morals, but they'd be terrified of losing their licence.
See the link below for TransUnion's and Equifax's reporting periods in Quebec.
http://www.fcac-acfc.gc.ca/eng/resources/publications/budgetMoneyMgmt/CreditReportScore/UndersCreditScore-eng.asp