If there is no deal, there won't be a withdrawal agreement. The withdrawal agreement is a part of the deal. No deal, no withdrawal agreement. The EU has made it very clear: "Nothing is agreed until everything is agreed".
The UK government amended the UK Immigration Rules to make provision for EEA citizens and their family members and will be trialled in certain limited areas (primarily North-East England) from next Tuesday. I think the crucial difference will be that the EEA citizens and their family members will need to apply for documentation as opposed to acquiring status automatically. But the requirements for the application will be broadly in line with that of the existing EEA Regulations.