Short answer: Inquire about buying the business out from your boss.
A person does not reach the point of closing a business lightly. They have gone through a lot of soul searching and no doubt a lot of money trying to save it. If you feel you can resurrect the business, you should see if you can buy it from the previous owner. Otherwise it's not your money that's at risk.
If the owner is looking at closing it down, you may be able to purchase at it a fair (and above all equitable!) price and retain the business's goodwill it has built up among customers, and you can implement whatever reforms you like. I don't know your financial situation or if you either have or could borrow the funds, but that way you have total control over what reforms you wish to introduce.
You may however find that running a business is not as easy as you think, there is a lot of responsibility when you have employees that need to be paid each week whether you have money come in or not!
As per comments where it's unlikely you can raise the funds to purchase the business, what you will need to do is to present a 1, 5 and 10 year plan to your boss as to how you plan to save the business.
You need to incorporate:
- How you plan to reduce costs (including any redundancies you will make and how much terminations will cost)
- How you plan to build revenue
- How long before your plan starts to produce a return
- How long before your plan covers the additional outlay
- What you expect to get from it
- How you are going to help make these things happen.
You need to prove to your boss why the risk is worthwhile, and how you plan to mitigate that risk. You need to give figures. Be very specific and be very conservative. Take your most conservative profit figures and halve them in your projections. Most people tend to overestimate how much impact they will have and how long it takes to come back into the black.