There are three types of patent searches
I.  Prior art patentability and Novelty search which is generally done before finalizing the invention or the patent specification also know as constructive reduction to practice. All patents, publications and markets all over the world are searched for this purpose.  The fact that the patent is foreign or has expired is irrelevant to this search. This is the most affordable type of search. It has 3 purposes:
(i) To make a GO NO-GO decision on filing a patent application
(ii) To improve the invention by piggy backing on the ideas of other similar inventions
(iii) To increase the chances of getting a PATENT and to reduce the patent prosecution costs by hitting the scope of the claims right on the head of the nail so to speak.
Even a prior art patentability search should not be limited to U.S. Patent collection but should cover in theory all publications or public disclosure of all countries in all languages regardless of how old and even common law folklore knowledge handed down by word of mouth from centuries and millennia.

II.    Infringement   Searches   are   generally   done   before commercialization or investment of huge sums of money in tooling and advertising etc. Only unexpired patents in the applicable venue are relevant to this search. Often it is necessary to draw claims chart of each patent found, which is very “Intellectual” Labor Intensive task. One of the advantages of such a search to the client is that it obviates charges of intentional infringement and hence avoidance of treble damages.  This is true even if the inventor-entrepreneurs is strictly making, using and selling the invention strictly according to his own PATENT.

The rational behind this is that your patent may be an improvement over somebody else’s unexpired patent. The good thing is that in order to practice your own patent you are liable only to the first patent owner but a third party must pay royalties to you and the first patent owner unless the third chooses not to incorporate your improvement. That is why the PATENT right is not an affirmative right to make, sell and use your invention but a negative right to exclude others from making selling and using your invention in the applicable venues.

It should also be noted that papers and patents do not infringe only products infringe. The term infringement should also not be confused with Interference in the United States Patent office which is litigation procedure in the patent office to determine first true sole inventor based on first to conceive and reduce to actual or constructive reduction to practice with due “Diligence” which very subjective and fact dependent. This interference proceeding is unique to USA and does not apply to other countries as USA is now the only country which is based on first to invent concept rather than first to file.  The cost of such a search is generally a many tens of thousands of dollars but is only small percentage of marketing and manufacturing costs, especially when the PATENT right includes right for INJUNCTION which makes most of patentee’s investment worthless because all hardware becomes scrap metal and all marketing and advertising expense instead of becoming “goodwill” turns into “badwill.”
III.  Patent Validity searches are done immediately before initiating a law suit, or after one is served with a law suit for patent infringement. This search is akin to finding the proverbial needle in the hay stack. Its cost is often many hundreds of thousand of dollars but a very small price and according to some even a  “BARGAIN” compared to what’s at stake. Often times it involves translation of apparently close foreign documents and patents into English for the first time.
CAVEAT: This is brief synopsis is not intended to be legal advice for which you should consult a qualified IP Lawyer before applying this information to your circumstances.