This guy I have been dating for 5 months said he loved me even though I didn't say it back he still meant it we spent almost every day together I had so much stuff in his apartment and he had stuff at mine. It was a great 5 months not much fighting at all and I really fell for him. Then there was a death in his family his family and he began to act differently 2 months later we got into a little fight and he told me his phone wasn't working properly so he would Facebook me to talk on messenger for a day until it gets fixed. 2 days later he didn't call or text me so I called him and he didn't answer, then I texted him an he didn't answer so I went to his house and he texted me saying"i know what u did and i refuse to answer the door" then he didn't talk to me didn't answer texts/calls and would not talk to me when I went to his house. His friends told me someone went up to my boyfriend telling him I cheated on him but I never did and tried explaining this over an over to him but he refuses to talk to me. Is there any way to get him to talk to me, I tried writing him a letter, texting and calling and leaving voice mails. Why would he just ignore me and not give me any closure on ending the relationship its been almost 3 weeks since he stopped talking to me and I have no clue why we were going so well until he started to ignore me :/

If he would believe something like that about you coming in the form of "he said" and not have the guts to even discuss it with you, who needs that!
He is either grieving over the loss in his family, immature or is looking for a reason to end the relationship.
You may not get closure but you need to stop contacting him and move on.

From experience... usually the accuser is the one who is guilty. Move on.