Yup you can write a garbage collected interpreter for a programming language with no unsafe code at all, even for languages that have complex data structures like doubly linked lists in them.

Using something like a slotmap to store the languages objects in is what I would do, and your GC would just involve removing values from the map after marking everything that's reachable.

The popular slotmap crate on crates.io does contain unsafe code but nothing about the data structure inherently requires unsafe.