You can find who the title company was by checking the deed when the property was bough, the deed will tell you who (typically the title company) recorded the deed, and hence which title company issued the tile policy.
This will cost you nothing. The title insurance should cover encroachments.
A few points that might help you.
If you do not have money I would look up free legal aid (see link below - ask the attorney's office for a referral).
Second, it is not unusual for claims like this to come up when a property is being sold. Let's just say that some people "coincidentally" find out that you "have to sell" and take the opportunity to "help themselves" to some cash (just my opinion).
Third, you need to discuss your situation with an attorney. If someone has occupied (trespassed) or openly used someone else's property for a period of time, and no one says anything, then the case can be made that the user has the right to use the property. I do not know the details, and you do not need to give them here. My point is that, as crazy as it may sound, you might be able to get away with it.
The other side of the coin is that if in fact a previous owner built the home and two feet is on your neighbor's property, you may have a real problem. We had a case in my home town in which the new owner had to remove the affected portion of his property AND comply with the setback ordinance.
Set back is the distance from the wall of your house, to your neighbors property. For example, in my town, the edge of the house needs to be 3' from the property line. So it my house was two feet over the property line, then I might have to trim 5 feet off my house. Theoretically the city building inspector would not have approved the building permit for a property that encroached on the neighbor's land, so it sounds as though there might be more going on here that meets the eye.
A trip down to the local Deparment of Building and Safety might be in order. Ask for the building permits for your house and take them to the attorney.
Talk to your neighbor... are they opposed to giving up the 2ft? Does this impact them negatively? Talk to an attorney ASAP. You want to avoid any lawsuites if possible... from either direction. Hope this helps.