I was staying in a house for a few weeks and moved out a week ago. I got a text message this morning saying they found a drug spoon in the trash can.

Law enforcement and/or the state can charge a person for finding something in the person's trash can.  But the more important issue is whether you can be convicted.  If there is enough evidence - other than merely circumstantial evidence, it is possible to be convicted.  But if, after you moved out of the house, others had access to the house or trash can (and, assuming nobody saw you put the spoon in the trash can), the evidence would only be circumstantial.  A person cannon be convicted when the only evidence is circumstantial evidence for which there is any reasonable hypothesis of innocence.  So if, after you moved out, others had access to the trash can there is a reasonable hypothesis that somebody other than you put the drug spoon in the trash can and you never possessed the spoon.  Then the state should not be able to convict you because that would be a reasonable hypothesis of innocence.  However, if the state has a witness who claims to have seen you put the sppon in the trash can - and who notified law enforcement, who then finds the drug spoon in the trash can, the state would have a better chance of getting a conviction.  There are still other defenses to be explored even under that scenario.  For instance, how can the state show that you were aware it was a drug spoon or that it had drug residue on it.  Unless the state has enough evidence to show you were in possession or control of the spoon and you knew it had illegal drugs on it, it is doubtful the state or law enforcement would try to file charges.  Also, many law enforcement agencies/state attorneys will not file charges when there is only drug residue -- but, beware, others will file on residue cases.