What are some factors that would cause employment to increase but GDP to decrease?

Toshia Metzker: The decline of productivity is the main reason. The government intervenes the labor market to increase employment during the time that the economy has structural problems. In some countries, the productivity is negative for some years. The increase in employment will not cause an increase in GDP,but reduce it.

Aubrey Tirri: Eliminate minimum wage and pensions. Minimum wage decrease would decrease wage more than the number of jobs created would make up for at least short term, and elimination of pensions via SS or state run equivalents would force elders back to work, mostly in low paid jobs, to partially make up for money not received. Elders mostly spend everything they get, plus they dig into savings, so they will spend less if they get less.

Adan Stribble: the only employment which doesnot contribute to the GDP, is government jobs.( in fair society)