We usually wear two malai when we start our fasting. The malai can be Thulasi malai or Rudrahsha malai or Spatika malai. You can wear a combination of these too. The reason we were two malai is because we need to have our mala around our neck for the entire viradha kalam (Fasting period). God forbids, if one mala is broken or comes off your neck, the other will be there to make your fasting to stay intact.
This is the reason we wear thunai malai.
You will also see people wearing only one mala, this is also allowed. In this case, there is no thunai malai.
Worst case, if your mala comes off your neck, chant "Swamiye Saram Iyappa" and put back the mala. If the mala is cut, hold the mala in tact, tie the two beads where it is cut using a thread from your cloth. You can mend it later. Do not feel bad about it. Leave it to Iyappan and continue your fasting.
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