I don't think you have to notify your clients by law but you should. You shouldn't leave your clients high and dry , it will give you a bad reputation. It isn't very hard to send out a mass text. I would seriously consider notifying your clientele.

It is not a legal requirement to inform your customers that you are closing down. It is however good customer service to notify your customers of the closure of your business and contact details in case they need to contact you at a later stage. Just be sure to honour all of your existing contracts before you close.
Yes, I agree with you on this. It's only a form of courtesy to inform your loyal clients that you're closing shop but I don't think you are required by law. However, it would also be good to inform your clientele about it especially if you're branching to other industries or if you're moving somewhere else to start a new business. Who knows they might even be interested in your new venture, then you would already have gained a new client base for it.
I have found that you are abided by the law for notifying the clients about it. However, it slightly varies from country to country. And In my opinion you should notify your customers that soon your business is going to be closed. It will create a great impact on them. And might be helpful for you in future, if you again starts a new business and at that time you need clients for your business.
It is a good practice to do so. By doing so, at least you do not seem to burn bridges with your clients. You might need them in the future again. Regarding the consequence of this matter, you should check your state's law regarding closing a business.
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