Few threads ago, someone mentioned if you were not able to get an acceptance from any prof/university after passing the first interview, the gov't (mext? or embassy?) will find you a prof/uni.
I'm just wondering if anyone has been placed through this method? How often does this happen? It just seems to me that if you cannot get a LoA on your own, very likely you will be rejected? Purely my assumption, so can anyone back me up? haha.
Please read Section 6 of the Official Guidelines: Placement and Research Guidance at University.
At the end of the day, you'll realise that almost 90% of what you need to know has been clearly stated on the 4-page guidelines. That is the official guidelines used by your respective embassies and MEXT Japan. Unless advised otherwise by your embassy (as in the case of the english/japanese written exam), you should heed the advise of the guidelines closely.
To further answer your question. Say, you've tried all the best you could, sent emails to 50 or more professors but still hasn't gotten any positive replies, your embassy might ask you to write a letter on why you are unable to secure the LoA, they will still submit everything to MEXT Japan for reviewing (even without LoA, but they will have to explain your case). In this case, i'm not sure whether your embassy will choose to put you as a substitute instead (do check with them).
BUT, as mentioned in the guidelines, MEXT will try to place you in the Universities of your choice, should that fail, they will again TRY to place you in other universities NOT in your preference. If all should fail within the available time, you will not be selected as a grantee.
In short, to make sure nothing bad happens, by hook or by crook, get at least one LoA.