A refractory patient by definition does not respond to the treatment. So it is expected to have PFI values closed to 0. So if a patient on  January 1st starts chemotherapy and on April 1st  did the clinical evaluation, stating that the disease progressed, this patient is refractory with a PFI=0 (progressed on treatment, no disease-free interval). Sometime, you may categorize as refractory even patients relapsing shortly after treatment (for example with a PFI

Your question is not fully clear to me, or the problem is maybe simpler than the interpretation by Cristiano.

- If you wish to calculate the mean PFI for patients that recurred or progressed since treatment, you could simply take the mean PFI for this subset of patients. However, the clinical relevance of that knowledge is probably small. Do not use Kaplan-Meier for this calculation, since by excluding patients that did not recur, you wrongly define the patient number at risk (the denominator in the KM product-limit estimator), (You can tell because the survival curve per definition runs to zero).

- It is clinically usually more informative to report the progression free interval for all  treated patients, using the Kaplan-Meier method. Therefore you have to define a separate event-censor variable (1=recurrence or progression, 0 = no event), and a time variable, which is PFI for recurring patients as defined above and survival-time for all the other patients.

-Beware of the pitfalls in reporting progression free survival and time to progression (see a.o. Saad & Katz, Ann Oncol 2008;20(3): 460; Hotte et al, Curr Oncol 2011; 18(S2) and many others). Depending on the clinical question, Relative Survival is usually a better way to estimate disease specific survival.

You can use Kaplan-Meier survival analysis to determine the median survival time, i.e., the time (e.g. years since last treatment) at which 50% of the patients have relapsed.   It is also common to use five-year survival, or three-year, or even one-year disease-free survival rates---e.g., the percentage who survive three years disease-free.    The rationality depends on the type of disease.  Breast cancer has a long median survival time and five-year survival rates (after treatment) are often used.  Lung cancer is much more fatal  and six-month survival is often used.  And of course you must be careful to ascertain the status of all patients if possible and define the cause of death:  death from the disease, death from any cause, etc., and there will sometimes be some patients lost to followup so you don't know if they survived or not.   And yes, the date of progression minus the date of last treatment will give you the time (e.g. months) of progression-free survival.   Have a look at the literature regarding the disease you are investigating and see what is commonly-used, e.g. three-year progression-free survival rates, or simply the median progression-free survival times (usually not the mean survival time because it is not normally distributed---but it depends on the study).  

Also be aware of length bias or screening bias in your study.  If you are periodically screening patients after their last treatments have ended, you may detect recurrences that would be diagnosed much later, from symptoms alone, in those who were not screened.   But if you are screening all survivors at the same intervals, for example every three months, then this bias should be eliminated---except that for some diseases (prostate cancer perhaps) there could be a long pre-clinical, symptom-free period where they don't know they have a recurrence unless they're screened for it.   These aren't fatal flaws - just keep those things in mind when you interpret your results.  

I also agree with Lucas about the difference between progression-free survival and time-to-progression.   If many patients die from something else before they have disease progression, this will under-estimate the disease-free survival period.  If you do not allow enough time for disease progression to occur, then this will weaken your study.  Again, see what the literature says and aim for what is commonly used.