First and foremost the employer wants to fill their vacancy. They will reach out to someone they declined and say that due to some unforeseen circumstances, they have another vacancy now (just as they would do if you died, or if someone else happened to quit that week) and ask if the person is still available and interested.
Then one of two things will happen. Either they will quickly fill the spot with a great person, in which case when they think of you at all it will be to say "we really dodged a bullet there", which is not very flattering, or they will have a nightmare where all the good people have taken other jobs and they have to re-advertise and re-interview and when anyone thinks of you it will be with resentment and scorn. The absolute best you can hope for is that they will forget you. If you want to work for them someday, but not now, then that's generally a foolish hope.
There is one exception though. If you want to work for them someday, and intended to work for them, which is why you accepted, but then something tragic and enormous happened, you may have a positive path forward. I mean like "both your parents died and you have to move to their city/country to raise your younger siblings" or "you have to be in the hospital for months and then years of rehab" level of enormous. Something that anyone can see at a glance makes it impossible for you to take the job now. If that is your case, you contact them immediately and say "I was so thrilled to be hired by you, and so looking forward to starting, but [thing] has happened and so I cannot. I will let you know when I am available again, in 6 months or a year, and I hope there will be a similar position with you I can be considered for."
If your reason isn't (a) out of your control, (b) something even a person with different cultural norms would instantly agree keeps you from working there, and (c) something with a long enough duration that you're not just asking to delay your start date a few weeks, then don't try this. For example, if you got a better offer somewhere else, go ahead and take it, but understand, that first place will very likely never (well, ok, 5-10 years, people move on) want to talk to you again. It's ok. There are lots of companies.
Tell them as soon as you can, as politely as you can. Don't tell them you got a better offer. Just say "unexpected circumstances." If it's not a better offer, then tell them the reason (need to be closer to my parents after my father's sudden illness, need to move to another country because this one no longer lets my fiancée visit, need a less stressful lifestyle while I recover from a car accident) in the hopes they won't hold it against you too much or for too long.
I see now in comments that your reason is "the salary isn't what I was verbally offered and verbally accepted." I'll leave the rest of this answer in place for other readers, but in your circumstances I would reply "the salary in this letter isn't [salary], which what I was verbally offered and verbally accepted. I can't accept this offer. Perhaps this is a clerical error? I look forward to a written offer that matches the verbal one, so that I can accept it and still start on [agreed date]." Then let them take the next step from there.