Why would investors go for that? In case of no investment, the company goes under, so you get 1% of $0. Therefore, you should be happy with pretty much any kind of dilution, new investors can easily force existing shareholders to get e.g. 0.1% of $5m.
That's why you don't speak to one investor only. Investors want to invest to make money and they compete against each other (if the company is interesting). Yes, if the situation is "please give us money or we're dead tomorrow", the negotiation position is going to be bad, but that would be because of mistakes made earlier (i.e. not talking to multiple investors, not talking to them early enough, not understanding when the money is going to run out etc).
