I can see why these is both abusive and frustrating as there is very little you can do to stop an investigation and this can be used a toll to harass small businesses by disgruntled employees.
The only way to stop the inspection unless you file an injunction with the court to stop L & I. I would also want to file an injunction against harassment against the employee (https://www.courts.wa.gov/forms/?fa=forms.contribute&formID=66)as well as report any criminal activity the employee was engaged in.
“An injunction is a court order requiring an individual to do or not do a specific action. It is an extraordinary remedy that courts utilize in specialcases where preservation of the status quo or taking some specific action is required in order to prevent possible injustice. For example, in a custody case, an injunction may be used to prevent a party from removing a child from the country. Injunctive relief is an equitable remedy granted when money damages are not able to compensate the plaintiff's violation of rights if an injuction is not granted. Failure to comply with a notice of an injunction is punishable by being held in contempt of court.
There are two types of injunctions: a preliminary injunction and a temporary restraining order (TRO). The purpose of both is to maintain the status quo --to insure a plaintiff that the defendant will not either make him or herself judgment-proof, or insolvent in some way, or to stop him or her from acting in a harmful way until further judicial proceedings are available. The court uses its discretionary power to balance the defendant's due process rights against the possibility of the defendant becoming judgment-proof, and the immediacy of the threat of harm to the plaintiff Courts can also issue preliminary injunctions to take effect immediately and effective until a decision is made on a permanent injunction, which can stay in effect indefinitely or until certain conditions are met. In many jurisdictions, plaintiffs demanding an injunction are required to post a bond.” http://www.uslegalforms.com/injunction-forms.htm
Here is more information on injunctions http://www.ehow.com/how_5707602_file-civil-court-injunction.html
I am not sure why they are insisting on continuing with the investigation based on the information that you provided.
My suggestion would be to hire a local attorney to assist you in fighting frivolous allegations from being pursued by disgruntled employees.
I would also file a complaint with the State Attorney General advising them that they are putting small business in jeopardy of harassment for unfounded claims. The Attorney General is the top law enforcement official in the State. https://fortress.wa.gov/atg/formhandler/ago/ComplaintForm.aspx
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