I don't know about that. When I made that there was always withholding and we have never not withheld according to their W4s. I can't imagine taking the liability of not withholding on as an employer.
Most employers, including the government, withhold based on what they project to pay you during the year, as if the job you work for them is the only job you have had, or will have, all year. If you will earn only $5,000 from them before the end of the year, they aren't going to default to withholding anything at all, if you are actually an employee as opposed to a contractor.
You can of course claim fewer dependents than the W4 would indicate you could, or ask for additional withholding, if you know full well that on top of that $5000 from them by the end of the year starting in, say, September, your previous job had paid you $25,000, or you had two other $5,000 short-term jobs with other employers.
A little awareness of this will avoid the problem, since you can either claim fewer dependents than the W4 permits, or ask for additional withholding to cover the possible gap.