Layer-2 is a chain that derives from layer-1. There is no layer-2 without layer-1.
1. Layer 2 depends on layer 1. If layer 1 stopped operating (e.g. doesn't create new block), it would halt the layer 2 as well.
Conversely it is also worth noting that while L2 is dependent on L1, L1 is not affected by anything that is happening on L2.
This is one of the main reasons for L2 in the first place: To be able to add new features (which may be related to scalability, privacy, smart contracts or whatever else) without having to make potentially breaking changes to the base layer.