I am assuming, for the purpose of this answer, that you are talking about actual (attempted) suicide - rather than (physician or associate) assisted suicide.
With regard to the U.S., various states at one time or another did have the act of attempted-suicide listed as a crime; some even as a felony, although I cannot find a single case of actual prosecution (of attempted - obviously you cannot enforce a law against actual suicide since the actor would be deceased). With that said, currently there is no law against the act of committing suicide in any state in the United States. I did a full Lexis search. Suicide (attempted suicide) is considered a mental health issue rather than a criminal one; hence, a person who is thought to be suicidal is subject to well being checks by fire, police, social services, and other like entities/people and are also subject to civil commitment and mental health holds if they are thought/found to be a danger to themselves or others.
To that end, the reason police can enter a dwelling without a warrant under these circumstances, is to do a well being check. If they have a reasonable suspicion that someone may be attempting to kill themselves (a family member, friend or a neighbor calls and says they believe you're are in eminent danger of harming yourself), the police may enter the premises and bring them to a hospital, even against there will. They can be held (at a hospital) to determine if they are of "sound mind". Every state has some form of civil commitment (statutes) and some limited amount of time a person can be held for observation (again, at a hospital or treatment facility).
I do not believe this is a typical ruse used by the police to enter premises without a warrant. Why? Not because all police are above skirting the laws against warrantless searches; however, there are just much easier means to accomplishing that end, if that is what they are going to do.
Yes, if evidence of a crime is in plain view while the police enter for a well being check (or any other legitimate reason), the individual can be charged with that crime. However, most police officers are not going to charge someone if they see (a usable amount of) drugs, paraphernalia, or evidence of some other low level crime. This is true since (1) they are already in crisis and (2) they are there for the very reason that they have information they may not be of sound mind, hence potentially not criminally responsible. If they walk into a meth lab or a murder scene or some other serious criminal scene, ...well that is different and all bets are off.
The bottom line is while this may have happened somewhere sometime to someone....this is not a practice I would be worried about.