Issue on conditional PhD admission I am an international student who has recently been officially admitted to a prestigious school in USA as a PhD candidate. I have sent them my transcript except my last year, which I was passing my courses by the application time. I am now in the second semester of that year. I haven't failed any of my courses in the first semester of that year, but I have failed the semester. The failure grade for a course is 10 from 20 and the failure semester GPA is 12 from 20 and my semester GPA is less than 12. The truth is I had too much work, TOEFL, GRE, IELTS, national entrance exam and also I was hospitalized and lost one of my courses in medical drop and other exams as a matter of fact to being ill! Please also do note that I will be matriculated in time and without any problems! In my admission form there is a sentence where it is said:

This admission is offered subject to your maintaining your present level of academic achievement. If you have not already done so, you must provide proof of satisfactory completion of any studies in progress.
In the conditions of admission part: --verification of all your previous post-secondary degree(s) earned outside of the United States is required. You must satisfy this condition of admission by engaging the International Education Research Foundation or World Education Services to verify your credentials.

I wonder what this sentence means. Does it mean that in my case, which I have had a rough semester, I should be worried about my admission and they will reject me because of my first semester bad GPA? Does a bad semester in the last year of B.S mean that you will lose your admission? Or is it just saying that you should finish your B.S and attend your new university in time? I should say that I have received my I-20 form and official admission!
Will they consider my case or will they just reject me even if I bring evidence of this fact? I am asking this because I have other admissions and it is best to know where to put the eggs. My question is how much should I be worried. It is also useful to say that this happened before my admission came and it is not because of having a good time.
I do not know what they will do in your case. However, in general, the procedure is such that when the application process for PhD happens, most students doing Bachelors or Masters degress in other countries are in their final year and do not have grades to send. However, if you do fail, then the offer of admission no longer stands, in general. 

For a PhD program, the minimum required standard is a bachelor's degree and if you fail that degree then why would they allow you entry? Having said that, now consider this. In certain countries, there are make-up exams for failed courses in a particular semester. If these make-up exams are taken before your offer of admission stands, i.e. Fall 2013 then you are good to enter. If not, then its bad luck for you. An offer of admission to a doctoral program only stands (in general) for that mentioned semester. You could potential defer the offer of admission another semester or year in order to take the make-up exams and then join the program. However, your chosen program may not allow this or may not have funds for you if you choose to join at a latter stage.

Basically, it all boils down to this. Contact the department immediately to ask for advice and tell them what options you have to finish your BS degree at home and whats the fastest route thats possible. Then see, what they have to say and take it from there. I speak from anecdotal evidence of a close friend who was forced to leave the offer of admission because he failed a couple of courses in his final year.

Do not try to fake your way through. I-20 or visa means nothing really for this problem and you will not be checked in general for proof of degree during your visa application process. But, be rest assured that you will be asked for proof of bachelor's degree once you join the program.