Will data overflow into attached block storage if instance storage is reached?

I have a Linode instance with a shared CPU, 8 GB of RAM, and storage that comes with it. I have attached a block storage instance of 120 GB with it.

I wanted to know how the storage works if the in-built storage of an instance reaches its limit. Will the remaining data directly go into attached block storage, or do I have to configure it?

When I see details with df -h it shows the following data:

root@localhost:~# df -h
Filesystem      Size  Used Avail Use% Mounted on
udev            3.9G     0  3.9G   0% /dev
tmpfs           796M  964K  795M   1% /run
/dev/sda        157G   11G  139G   8% /
tmpfs           3.9G     0  3.9G   0% /dev/shm
tmpfs           5.0M     0  5.0M   0% /run/lock
tmpfs           3.9G     0  3.9G   0% /sys/fs/cgroup
tmpfs           796M     0  796M   0% /run/user/0

And the fdisk -l command shows the following:

root@localhost:~# fdisk -l
Disk /dev/sda: 159.51 GiB, 171261820928 bytes, 334495744 sectors
Disk model: QEMU HARDDISK   
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes


Disk /dev/sdb: 512 MiB, 536870912 bytes, 1048576 sectors
Disk model: QEMU HARDDISK   
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes


Disk /dev/sdc: 120 GiB, 128849018880 bytes, 251658240 sectors
Disk model: Volume          
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes

Thanks for the help