- usually you get dropped to initram terminal due to lack of drivers to load the system from the partition it's located on. E.g. in case of custom Live DVD/USB it may be lack of drivers for DVD-ROM, even though the initramfs got loaded from it.
busyboxis used in initramfs, but it may have some utilities compiled out. That may be dealt with by re-compiling busybox. But since it is for debugging purposes, don't create a whole package out of it (it may need some installation scripts and whatnot), and certainly don't callmake installwhich does nothing useful in case of busybox. Instead better manually replace thebusyboxbinary that belong tobusybox-initramfsor similarly named package.