Why do (don't) stricter emission limits lead to job loss?
I am not knowledgeable of the mechanism and exact details of the emissions paraphernalia, but the sector's worry makes perfect sense. Stricter regulations lead to or contribute to
Stricter emission regulation entails a greater probability and/or magnitude of fines and sanctions to non-compliant companies. To avoid those sanctions, a company will be forced to spend additional resources to (1) replace technologies that are otherwise perfectly operational, (2) focus on expertise that distracts that industry from its core business, and (3) fund expenses that result from the increased overhead. The question is where those resources will come from.
Car makers may opt to pass that cost to consumers. However, that decision predictably will push sales down, thereby leading to overcapacity of labor and consequently layoffs.
Alternatively, car makers may decide to absorb the new compliance costs and leave the price of cars unchanged. But the prospect of reduced profits would prompt stockholders to sell their stock, thereby weakening the car maker's ability to meet its financial obligations. To cope with (or avoid exacerbating) this imbalance, the car maker has to reduce costs; and the readily available alternatives to that effect are layoffs and a freeze of new hires.
Furthermore, for car makers with significant reliance on exports, compliance with stricter regulations tends to hinder their competitiveness especially with respect to non-EU car makers which are not subject to akin regulatory constraints. Thus, EU car makers will lose [international] market share, most likely impacting its ability and interest to keep that much of its labor force.