If they want to replace the old pipe rip their arm off, bend over backward and point the way.
The main sewer is the one thing you really really do not want to go wrong on your property.
because we use less water to flush, because people flush things like baby wipes, nappies, cotton buds, cat litter, tampons, cooking fat, pipes blow, especially old ones,
Get them to add inspection chambers(manholes) at the points where the main enters your property and leaves your property, and if that is a long distance, add one in between, this will totally future proof for any blockage problems.
you are responsible for the bit waste pipe from your house until it meets the main, even if your neighbours joins this, if the issues are coming from age, thing about using this opportunity to updating them, you may well be able to convince them to do it as a part of the package, do you know where your waste runs, and joins the main,
the new systems are click together so easy to install.
Take lots of pictures of your garden before anything starts.