When a fence or other structure crosses the property line it's called an encroachment. A fence can moved to remedy the situation, but when a building or other major structure encroaches, the alternative to removing the portion that encroaches may lie in an easment agreement. This requires cooperation from the owner of the adjacent property. Payment or a trade of easments may be negotiated to allow the encroachment and obtain a marketable title policy. This may also require affirmative title insurance, explained as follows:

By Christopher Hinton, National Agency Operations Counsel at Title Resources
Sometimes referred to as “insuring over” or “insuring around,” affirmative coverage is issued by the title company – usually at the request of the mortgage lender – to protect the insured against specific, identified title defects, typically set forth in Schedule B of the title policy.  Affirmative coverage can be a powerful tool to successfully close real estate transactions in the face of identified title defects. 

Unlike standard coverages or endorsements to the policy, granting affirmative coverage is a decision by an underwriter to accept the risk of loss posed by an identified defect, such as an encroachment, pre-existing lien, indefinite or vague easement rights, or incorrect legal descriptions contained in a prior vesting instruments.  The affirmative coverage is granted by adding customized language to the policy, thus insuring against loss caused by the specific, identified title defect. 
Affirmative coverage gives underwriters the flexibility to accept specific identified risks, without accepting an entire class or type of risk, and allow transactions to proceed.  Underwriters may grant affirmative coverage in situations where the risk of loss is extremely low, but removal of the defect cannot be completed prior to closing.  For example, a prior unreleased mortgage lien, for which there is evidence of full satisfaction, may remain in the chain of title.  Due to the lender’s processing time and the municipality’s recording schedule, the release of the lien may not be able to be completed prior to the closing.  In these situations, affirmative coverage allows the removal of the title defect, the unreleased lien, to proceed without impacting the closing schedule. 

More commonly, affirmative coverage is granted in situations where the underwriter determines the likelihood of loss resulting from the defect is extremely small.  For example, an underwriter may grant affirmative coverage for a specific mechanic’s lien, without granting coverage for all mechanic’s liens, that has attached to the property because adequate bonds or indemnity agreements are in place to satisfy the lien.