Using GRUB's chainloader +1, results in the following error condition upon booting:

error: invalid signature

This is likely caused by GRUB not installing to the partition you specified.  (ie. grub-install /dev/sda4)

You can verify if GRUB is installed to the boot sector of a partition by using "dd if=/dev/sda bs=512 count=1 | xxd" or "dd bs=512 count=1 if=/dev/sda4 | od -Ax -tx1z -v" or "hexedit /dev/sda4"; and viewing blocks 0x1FE-0x1FF (000001FE-000001FF) and ensuring they contain "55 AA".  Or that the bytes before 000001F8 contains ASCII date relevant to the GRUB boot sector or whatever boot loader you are using.

A common reason why GRUB2 hasn't installed when using "grub-install" (even though GRUB has stated everything was installed fine), is that the grub-pc package was not installed and only grub-efi packages were installed.  So if you're using Debian, a likely solution is uninstalling the grub-efi related packages keeping the grub-common packages, and then either reinstalling grub-common packages are additionally selecting the grub-pc package to install.  Afterwards upon using grub-install, you'll likely now see some warnings when installing to any partition instead of the main disk MBR, and you should now also see the beginning sectors of the partition containing grub data!

Further reading, "Details of GRUB on the PC"; http://www.pixelbeat.org/docs/disk/; Pádraig Brady; Copyright July 28, 2005.  Enjoy the author's note concerning, "Note also the official grub docs on these disk areas which appeared about 7 years after I wrote the notes above."  I also agree GRUB2 isn't the most user intuitive piece of software!  For example, the above error I wrote about is initially very non-descriptive, leading to a number of possible solutions; above which is the most undocumented solution and yet likely the most trivial to solve.