To be accurate there is no such thing as a "failed" certificate..
Electrical certificates or minor works certificates:
Are issued following completion of some electrical alterations, to confirm that the alterations comply with the current wiring regulations.
In a domestic property situation there are some legal requirements for issuing electrical certificates that come under Part-P of the building regulations.
There are also electrical installation condition reports:
Which follow inspection and testing to verify the condition of an existing electrical installation.
And an evaluation is made to state if the installation is "Satisfactory" or Un-Satisfactory" for continued used.
There should be a page with a list of observations that are categorised as;
Danger present, Potentially dangerous, Improvement recommended or further investigation required.
Although wiring regulations BS7671 recommend inspection & testing at a change of occupancy..
there is NO legal obligation to have a condition report done..
and/or either party may choose or not to pay for an inspection..
So I assume you have an "Un-satisfactory" condition report.
with a list of various observations..
(Please note, although there are some industry standard guidance about coding observation,
there is an element of personal opinion of the person doing the inspection.)
A free download guide is available discussing some aspects of electrical condition reports,
which may or may not be of some assistance to your interpretations:
https://www.electricalsafetyfirst.org.uk/media/2149/bpg4-1.pdf
It is generally in the best interests of the purchaser to pay for a condition report..
BUT.. until you actually own the property you are dependant upon the goodwill of the seller to allow one to be undertaken,
as to do an accurate inspection involves disconnecting the power and opening up a sample of accessories to do various tests.
As both the seller and their estate agents want to sell the property to get their money and commission, it is not uncommon for a very basic visual-only inspection to be done, to try and suggest that an electrical installation is in better condition than it really is. Plus visual reports are in reality of minimal value to anyone!!
To answer the second part of your question..
There is NO obligation for anyone to have to do anything...
It is basically down to how the two parties are willing to negotiate the price around the perceived condition and value of the property.
Similar to buying a second-hand car privately..
It may have MOT or may not..
It may be in full running order or may not..
You may choose to get an RAC/AA/Other organisation to do a vehicle inspection before purchase,
or you may just buy it as seen!
The key factor is how many other people are wiling to pay the asking price!