For larger projects, the contractor is required to be bonded to cover things like this.
Is $1 a large project?
Since the amount at risk is the amount of the bid prior to yours, that should determine both the amount of any bond requirements and, if there is a sharp cutoff, the cutoff for the requirement for a bond.
the point of this process was procurement in increments less than $3,500 to avoid many regulations.
If lowest bidder is nowhere to be found, then the next lowest bidder gets the work.