There's a store near our home that has the "We're closing! Everything must go! Huge discounts!" Sign.
It has been on their store for at least 6 months.
Is it fraudulent or illegal to make such an advertisement when the store has no plans to close?
The jurisdiction does matter.
Generally, at the national level, the Federal Trade Commission prohibits deceptive advertising. From the FTC's website, "Advertising FAQ's: A Guide for Small Business:"
When can a company advertise a "going out of business sale"?
The short answer is: only when a store is going out of business. It would be deceptive to advertise a “going out of business sale” when a store is not going out of business. If a store in your area is advertising what looks to be a bogus “going out of business sale,” contact your state Attorney General’s office.
In their answer, they specify to contact your state Attorney General's office. Many states and localities have specific statutes that regulate "going out of business sales."
San Diego, California, for example, requires a permit from the San Diego Police Department whenever a business has a "closing-out sale." Their permit application indicates a list of the types of sales that are subject to the ordinance and closes with:
Or, any other term tending to convey to the public that upon the disposal of the stocks of goods on hand, the business will cease and be discontinued.
The permit in San Diego is valid for 60 days and the business is required to provide an inventory of all goods that will be sold as part of the liquidation sale.
The requirements of the city of San Diego are similar to many other jurisdictions. Some of these requirements are specified at the state level, such as Texas (Business & Commerce Code Section 17.45 Deceptive Trade Practices), while other states leave it to the localities.
California doesn't appear to have a statewide "going out of business sale" law but they do have other laws and regulations governing false advertising. California Business and Profession Code section 17500 prohibits untrue or misleading advertising. The California Bureau of Home Furnishings has promulgated regulations based on this statute to prohibit such sales to only include items that are
on premises, in the warehouse or in process from previous orders the date the sale is announced
This regulation for furniture retailers in California is common among the "going out of business sale" regulations in that it prohibits the closing business from purchasing new merchandise while liquidating and is one of the reasons that inventory lists are required when applying for a permit for a liquidation sale.
As a side note, I was always amused by a store on Fisherman's Wharf in San Francisco that had a "Going Out For Business" sign in their store window. I probably read it a hundred times over the years before I realized what it really said.
It might help you if you and as many people as possible understood to the difference between the terms "illegal" and "unlawful" which do not have the same meaning, or rather do not necessarily, have the same meaning, and tend to be confused, there being prescriptive and proscriptive and/or punitive laws; as often as not the term is illegal applies to the criminal law – punitive law. Local laws may well prescribe the form or manner in which representations are made about the sale of goods,and failure to comply with those prescriptive rules would make the representations and "lawful",and, depending on the circumstances, also possibly criminal offences attracting the epithet "illegal". Moreover local laws may proscribe certain forms of representations, generally speaking those that are fraudulent or misleading and penalising such, making failure to comply with them "illegal";and sometimes they overlap. If the representation is "unlawful" it may well render any subsequent contract based on it nugatory. It does not help when lawyers themselves confuse the terms, which is not altogether unknown viz.unlawful contracts sometimes being referred to as illegal contracts, see wagering contract and also so -called immoral contracts.
In my respectful submission it is simplest and most efficient if the use of term "illegal" is restricted to criminal offences, which are those actions or activities which are proscribed by some sovereign body such as a parliament or government,king,or chief. You will frequently encounter the faintly idiotic term "illegal war",which rather begs the question which sovereign body prescribed the particular war?– see also the comparatively nonsensical term "international law".