(Courtesy of Bob Crosby)
Negative free bids for 2/1 in competition after an opening bid do not make much sense to me as written. The responder can have a good hand quite often so the negative double with forcing good hands just complicates matters. However, there is a place for negative free bids. After an overcall by partner and an intervening bid, a non forcing free bid would be very useful for lead directing or sacrifice purposes.
Negative free bids complement fit showing jumps in competition after an overcall, If you do have your own suit and a fit with partner then jump in that suit. Otherwise your suit bid is a non forcing free bid.
KQJ1098 xx xxx xx
LHO opens 1 and partner overcalls 2, RHO bids 2. This is a negative free bid of 2. There is so much bidding that a rock 2 bid is very unlikely to exist. If by some chance you have one, you can make a snapdragon double showing the unbid suit and tolerance for partner's suit. Later on, bid spades to show your strength. There is so much bidding going around, I would rather play introducing a suit as a "negative free bid" not even forcing one round. This is both lead directing, finding a sacrifice or making a nuisance of yourself all in one negative free bid, If you do not play negative free bids, you have to bid 3 with this hand. Splinter addicts cannot even do that.
KQJ10x xx Axx xxx
This time 1 - 2 - 2 - ? but this time you bid 3 as a fit showing jump, if you play the bid after overcalls (recommended). Normally a new suit would imply a fit with partner and a one round force. With negative free bids it does not, so we use the fit showing jump. We do not play splinters in competition, so a jump can be a weak jump shift or a fit showing jump. If you go the "negative free bid" route you can play fit showing jumps with overcalls. My partners and I only play fit showing jumps as a passed hand but if we buy into "negative free bids" it opens the door for the bid after overcalls.
KJ109x xx xxx Kxx
With the same auction as above, it would be nice to stick your nose in with a negative free bid of 2. If you have a "real" 2 bid which you want to be forcing one round you are forced to double (cards) as per negative free bid theory.
The concept of negative free bids appeals to me when there is lots of bidding going on. Getting in there with your suit without forcing values makes a lot of competitive sense. The contortions with negative doubles for the good hands make the bid not worth it though, with 2/1 auctions. Overcalls are a different matter though just due to the low frequency with partner having a positive free bid. Negative free bids now make sense. Negative free bids and D.S.I.P. doubles go together. If you would double with cards, you do not need bidding a suit as a one round force.