You can enter in noncollectable status; this will not suspend the 10 year status. From the experience of many years of dealing with the IRS although a 10 year statute exists, it is not enforceable. As long as there is a balance due, it is going to remain on the books of the IRS.
You can go into non-collectible and it can sit there for 20, 30 or 40 years ( I have seen it multiple times). If there is something for them to put a lien on they will do it and it will forever remain enforce until the bill is paid in full. So you would be in a position of not being able to sell a house that had a lien on it without agreeing to pay the lien in full at closing.
If you elect to go on an installment agreement, they may agree to remove the lien. Generally they do not and it would probably be sitting with the lien until the amount is paid in full.
Did the tax office mention an offer in compromise to you at all? This might be a best option. If IRS does not think you can pay the full balance in a reasonable period of time (generally 5 years), they may agree to a reduced paid in full. Not likely to be the "pennies on the dollar" that you see on TV, but often I see where there is a reduction to just the tax paid and the penalties and interest go away OR you might be able to get a 40% or possibly even if 50% reduction. So you might get away instead of paying $10,000 you might be able to settle for $6000 and the debt paid in full.
With the acceptance of an offer in compromise it could be a lump sum payment that is required or it could be an installment payment for 24 or 36 months.
This would get rid of the debt over a period of time, the lien would be removed allowing for a house to be sold.
To qualify for the offer in compromise it needs to be apparent based on your current status that it cannot be anticipated by the IRS that the debt would be paid within 10 years.
I hope this helps. If you have a specific question do not hesitate to hit the need info button and ask. Otherwise, hit the accept button to close out the question.