If the salon owners are, in fact, in default under their lease, the landlord has a number of options in dealing with personal proety left on the premises. The landlord might obtain a writ of possession and have the tenant's property moved and stored. The landlord might enforce staturory lien rights (Sec. 54.021 Texas Property Code) or lien rights provided for in the lease. The landlord might also treat the personal property as abandoned and dispose of it in accordance with Section 93.002 of the Texas Property Code. Nevertheless, if you put the landlord on notice that the property is your property, that it does not belong to the tenant and that you are an innocent third party, the landlord would not be well advised to dispose of your property in a way that would wrongfully impair your ownership rights. I would send a certified letter, return receipt requested to the landlord identifying yourself and your property, explaining that the property is yours, not that of the tenant and demanding return of the property. I would follow up with a phone call or personal visit to the landlord's offices. The landlord may be liable for conversion if it disregards your rights after being placed on such notice. If the property is valuable, you should consult a lawyer to help you with the notice and demand.
Legal disclaimer: This answer is not legal advice, but is for informational purposes only. My answer to your question does not create an attorney-client relationship between us. Please contact a licensed attorney in your area for competent legal advice.
Send a registered letter to the owner demanding that the LL let the innocent third parties get their personal belongings. May be worth having an attorney craft and send it for added impact.
I'm not your attorney; my answer to your question includes assumptions. If you want me to be your attorney, I'm easy to find.