There is no reasonable situation where "by" would be an acceptable substitute for "until" in your example sentence. As others have pointed out, the only cases where you could use "by" are:
1) they decided to extend the negotiations by (x),
where x is an AMOUNT of time
2) they expect to decide by (x) whether to extend negotiations
where x is a DATE
Neither of these have the same meaning as your original sentence with "until". The second rendering above would mean that they have NOT yet agreed even as to how long to extend. (But your original sentence clearly indicated that they HAVE decided that question; i.e., they decided to extend the ending date of the negotiations to July 15.)
I suspect your puzzlement might not be with understanding how "by" and "until" work, but rather with understanding how "extend" and "postpone" work. To "extend" negotiations means to let them continue from now to a later date than expected. To "postpone" (or "suspend") negotiations means to stop negotiatiating now, but agree to "resume" at some future date.
They could agree to EXTEND, negotiations "until" (or "to") some date. This means negotiations will continue "until" then (they are expecting to finish "by" then.)
Or (and this is what I suspect you really meant) they could POSTPONE (or, more accurately, SUSPEND) negotiations "until" some date. This is the same as agreeing to stop negotiatiating now, and to RESUME talks "by" (on) that date. No ending date for the negotiations is implied.