Based on the manufacturer's youtube video for the app compatible with the cable:
This is a video guide for SmartLog(Blood Glucose Management Software) App represensted by i-SENS.
SmartLog App is a smart phone application which helps patients with Diabetes to monitor their health conveniently anywhere anytime. This app works with CareSens N NFC meter. CareSens N and CareSens N POP meters can also be used when using FTDI cable.
A FTDI cable typically refers to a USB to RS232 (TTL level Serial) IC FT232 (or other generations of the FT232 chip) created by FTDI. They also make other USB bridge ICs with similar functions.
Connecting a USB cable straight through to a 2.5mm plug will most likely cause a problem. as you have already seen.
If it's a simple straight through connector, it will have Ground, TX and RX. FTDI's official 3.5MM cable uses Tx {To device from PC}, Rx {From Device to PC}, Gnd (Tip, Ring, Sleeve, respectfully). With your multimeter, you can confirm the 2.5mm pinout by doing a continuity test between each section of the adaptor and your 3.5mm cable wires, then confirm the signal by checking for voltage between the three wires. The voltage it runs at is a concern because using a 5v signal on a 3.3V port might be bad.
Of course it could be more complex. TI calculators used a 2.5mm port for their Graphlink cables. It was able to connect to a serial port, but required 6 pins, resistors and diodes between.
If you had a cable to hack up, or even a meter to hack up, it would be easier. They occasionally pretty much aways give the device away for free, check with your doctor or the manufacturer's local sales rep.
Update: Based on the two links below, the pinout is more likely to be Tx from Device to PC, Rx From Pc to Device, Ground (Tip, Ring, Sleeve). Like a defacto standard amongst Diabetes Meter manufacturers. You need the USB to serial IC for the OTG cable, but you could use a serial port for the PC instead (I am not liable if you fry your meter).
http://pinoutsguide.com/Electronics/bayer_contour_pinout.shtml
http://www.diabetesforums.com/forum/topic/65566-abbott-freestyle-freedom-lite-data-cable-how-to-some-other-info/
Reading data from a glucose meter
USB cables are not simply "4 wires". They have certain properties that need to be met so that the data signals can travel through the cable. Your thick wires will not have the correct properties causing the data signals not to travel properly, instead they are suppressed and reflected resulting in the USB connection to fail.
Best Answer
Shutting off the power to such a device should not hurt it. After all, power can be interrupted for various reasons like a power outage, a breaker popping, and the like, so devices are designed for that.
Some complicated devices may have software issues when power is suddenly interrupted, but should not suffer hardware failure. For example, you shouldn't suddenly shut off power to a PC since that doesn't allow the OS to flush pending file changes to disk, allow device drivers to shut down their devices in a orderly fashion, etc. The PC will physically survive, but some files may be corrupted.
Routers and modems without mass storage devices are much less likely to have software issues with suddenly interrupted power, and should not get damaged by that physically. Cables are impossible to damage just by interrupting normal power. To kill a cable you have to put significantly more than the rated current thru it, which interrupting power doesn't do.