If you have a title search done during the time you are in escrow before you buy a property, it is possible that something is missed and one can make a claim against your property.
More likely, however, is that the previous owner has given permission to use the property of others in some way without recording it.
An example of this would be if the previous owner gave neighbors verbal permission to use a portion of the property for a specific use. Unless it is documented and filed, it is unlikely that the agreement will appear in the title search.
How Title Insurance Works
Companies offering title insurance and settlement services protect you from working with disabilities in the title.
This defect occurs prior to the date of your policy is issued and before you take possession of the property. Title agencies will study the history of the property to identify and fix defects in the title before they issue a policy.
If they find a defect in the title, defects will be repaired or registered as an exception to the policy. If it is listed as an exception, it will not be covered against future claims.
Keep in mind that this is very different from most other types of insurance such as homeowners insurance, which protects you from future events unseen.