I don't think it will.
Jim can issue new shares so long as the majority of shareholders agree (which is Jim agreeing with himself) and just not give you any. Consequently the percentage of the available stock you own is diluted, and you end up with less and less of the company. This is how it works in the UK (where I am).
Normally share dilution happens when new investors come on board and put some money in which increases the value of the company so the value of the shares doesn't really change. If there are 100 shares in the company and the company is worth £1000 each share is worth £10. If you own 40% that's 40 shares worth £400. If 100 new shares are issued and sold to an investor for another £1000 then the company is worth £2000 and there are now 200 shares still worth £10 each. Your percentage has dropped to 20% but the value of your investment is still worth £400 (ignoring the value of dividends, voting rights, etc). The same mechanism can be used to screw people though if more shares are issues without a commensurate increase in value.
If Jim issued himself more shares for a nominal fee, he would have to offer the OP the same deal.
Yes, share dilution might happen with genuine investors, but no he can't just dilute out the OP on his own to 'screw' him.