Recovering data from Mi 4c able to get only to fastboot
Success! Thank you @alecxs for help and resources.
1 Obtain a programmer
To successfully acquire all of the data from EDL you need programmer.
For Mi 4c it is prog_emmc_firehose_8992_ddr.mbn that can be obtained in (first?) official image of OS. I got it from file Xiaomi_Mi_4C_V8.1.3.0.LXKCNDI_20161213_China_5.1_XFT.zip on some random site. You can find it in the archive under folder Firmware/images/.
The full path in archive would be Firmware/images/prog_emmc_firehose_8992_ddr.mbn.
2 Get working Firehorse
I have got mine from repository: https://github.com/bkerler/edl.
Proceed with all instructions mentioned in the repository. (I personally used Ubuntu 20.04 as all of the stuff is easier to make work.)
3 Connect to EDL
Boot phone to fastboot. In case of Mi 4c that is my case  it is pushing volume down during boot.
When you enter fastboot and you can see your device with fastboot:
fastboot devices
In case of Mi 4c you can directly boot to EDL with command:
fastboot oem edl
4 Acquire data through EDL
When device enters EDL state you can test connection with programmer (in my case prog_emmc_firehose_8992_ddr.mbn). In loader parameter you are entering path to this file.
./edl.py --loader=prog_emmc_firehose_8992_ddr.mbn printgpt
When it outputs all of the partition then you are golden!
On my phone there is one partition named userdata:
userdata:            Offset 0x00000000c4000000, Length 0x0000000683bfbe00, Flags 0x00000000, UUID 07c2b899-1574-564c-2f46-e26a6378bdd8, Type 0x1b81e7e6
To acquire the partition use command:
./edl.py --loader=examples/prog_emmc_firehose_8992_ddr.mbn r userdata userdata.bin
The copy of user data just needs to be read.
5 Reading user data (userdata.bin)
Luckily for the phone Mi 4c you can directly mount the dump in Linux. For some other phones the process might not be so straightforward and you might need simg2img. But I am not 100% sure.
sudo mkdir /media/userdata
sudo mount -t ext4 -o loop userdata.bin /media/userdata/

To read the data you will need to get root rights as the data belong to non-existing or different existing users and you won't get access with your user.
sudo mkdir userdata
sudo cp -r /media/userdata/media/0/* userdata/

The path to the your data might be different so take your time to look around.
Done! All the data are now completely accessible.