That is not the case with most company out there. They will stop matching if the employee stops contributing. Foxbusiness explains it as this:
How Do I Maximize My Employer 401(k) Match?
Many employees are not taking full advantage of their employer's matching contributions. If, for example, your contribution percentage is so high that you obtain the $16,500 (year 2010) limit or $22,000 (year 2010) limit for those 50 years or older in the first few months of the year then you have probably maximized your contribution but minimized your employer's matching contribution. The goal is to reach the IRS limit while at the same time maximizing your employer's matching contribution and thereby maximize take-home pay.