Emily wants to sell her business. She has a business that could be integrated into another business. However, Emily wants to maximize her sale price. She is not likely to sell to another business.
Many businesses-for-sale are priced, at least in part, based on cash flow to owner. In most cases the owner actually works in the business, at least part time. So, the cash flow to the owner includes the wage or other draw the owner takes.
If a buyer is another business or an owner not wanting to work the business, this buyer is likely to not want to pay as much for the business.
So, poor Emily will not realize the best price for the business unless she waits. Sometimes waiting for another buyer is not possible or reasonable.
Obviously it could be that the lesser offer should be taken as it could be the only offer. Perhaps she can negotiate a consulting agreement for several years following, continuing to work to some degree and earning additional money.