TWR CTLR CLRED B737 FOR TKOF BEFORE A C172 CLRED THE RWY.

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FLT WAS #1 FOR TKOF; FO LEG; DUSK. A SINGLE ENG CESSNA WAS ON FINAL. AFTER THE CESSNA LANDED; ISP TWR INSTRUCTED THE ACFT TO TAXI CLR OFF THE RWY AT TXWY W. I OBSERVED THE ACFT TURN R AND EXIT THE RWY. TWR CLRED US FOR TKOF. AS WE ACCELERATED THROUGH 80 KTS WE NOTICED A BEACON LIGHT AT THE R EDGE OF THE RWY. THE FO ASKED 'IS HE CLR OF THE RWY?' I RESPONDED 'COME TO THE L JUST IN CASE.' AT THE SAME TIME TWR ASKED THE CESSNA IF IT WAS CLR OF THE RWY. THE CESSNA IMMEDIATELY RESPONDED 'CLR.' I HAD ALREADY ELECTED TO CONTINUE TO TAKE OFF AS WE WOULD BE AIRBORNE BEFORE TXWY W; AND AN ABORT WOULD INCREASE THE POSSIBILITY OF CONFLICT IF PART OF THE CESSNA DID EXTEND OUT OVER THE RWY. JUST GOES TO SHOW YOU; EXPECT THE UNEXPECTED; AN ACFT EXITING THE RWY MAY STOP WITH PART OF ITS TAIL; WINGS; ETC; STILL ON THE ACTIVE RWY. SUPPLEMENTAL INFO FROM ACN 466454: WHILE OPERATING A B737-200 FROM ISP; WE ENCOUNTERED A RWY INCURSION WITH A HIGH WING CESSNA. WHILE HOLDING SHORT OF RWY 24; THE CESSNA LANDED AND WAS INSTRUCTED TO EXIT THE RWY AT THE FIRST AVAILABLE TURN; AND TAXI TO THE RAMP. WE WERE THEN CLRED FOR TKOF. JUST PRIOR TO V1; I OBSERVED THAT A PORTION OF THE CESSNA'S ACFT HAD ENCROACHED UPON OUR DEP RWY; AND I BROUGHT IT TO THE ATTN OF THE CAPT. IMMEDIATELY THEREAFTER THE TWR CTLR TOLD THE CESSNA TO TAXI CLR OF THE RWY. AT VR I INITIATED A BRISK ROTATION AND WE AVOIDED THE CESSNA BOTH LATERALLY AND VERTLY. THE TWR CTLR STATED 'NICE JOB' AND WE WERE XFERRED TO DEP CTL. THE REMAINDER OF THE FLT CONTINUED UNEVENTFULLY. SUPPLEMENTAL INFO FROM ACN 465381: ON MAR/SAT/00; AT XA14 LCL I WAS ACTING AS THE CFI WITH A STUDENT PLT AT THE CTLS OF A CESSNA 172. ISP TWR HAD CLRED US TO LAND ON RWY 24; A 7000 FT RWY. AS WE MADE OUR APCH TO RWY 24 WE HEARD THE CTLR TELL AN ACR B737 TO HOLD SHORT OF THE RWY. AS WE WERE ABOUT TO TOUCH DOWN ON THE FIRST 500 FT OF THE RWY WE HEARD THE TWR CALL TO THE ACR B737 TO TAKE POS AND HOLD ON RWY 24. AS WE ROLLED DOWN THE RWY AND BEGAN TO SLOW DOWN I INSTRUCTED MY STUDENT TO SLOW THE ACFT TO MAKE A TURN ONTO TXWY B; WHICH IS WITHIN THE FIRST THIRD OF THE RWY; BUT TO MAINTAIN THE CTRLINE. AS WE APCHED TXWY B THE CTLR DIRECTED US TO TURN R ON TXWY W AND GAVE US THE INCORRECT GND FREQ. HE THEN CAME BACK ON THE RADIO TO AGAIN DIRECT US TO MAKE A R ON TXWY W; BUT HE NOW GAVE US THE CORRECT GND FREQ. SINCE TXWY W IS WITHIN THE LAST THIRD OF THE RWY THIS DIDN'T SEEM CORRECT TO ME. HOWEVER; AT THIS POINT WE HAD NOW ROLLED PAST TXWY B AND THE CTLR WAS ALREADY GIVING INSTRUCTIONS TO OTHER ACFT IN THE PATTERN. AT THIS POINT I WANTED TO QUESTION THE CTLR BUT WITH THE B737 HOLDING IN POS AND THE CTLR STILL ON THE FREQ TALKING TO OTHER ACFT I DIDN'T WANT TO STEP ON HIM AND CAUSE PROBS WITH ANY AIRBORNE ACFT. SO WE EXPEDITED OUR TAXI TOWARD TXWY W; AFTER BEING TOLD TWICE TO TURN THERE. WE WEREN'T HALFWAY DOWN THE RWY WHEN THE CTLR CLRED THE ACR B737 FOR TKOF ON RWY 24. BEFORE BEING ABLE TO TELL TWR THAT WE WERE STILL ON THE RWY HE IMMEDIATELY BEGAN TO COMMUNICATE WITH OTHER ACFT. I HAD MY STUDENT STEER THE AIRPLANE TO THE R OF THE RWY AND INCREASE SPD IMMEDIATELY WHEN I TURNED TO SEE THE B737 WAS IN FACT ROLLING TOWARD US. WHEN THE CTLR NOTICED HIS MISTAKE HE BEGAN TO ORDER US OFF THE RWY BUT NOT BEFORE THE ACR B737 HAD TAKEN OFF OVER THE TAIL SECTION OF OUR PLANE.