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They must have valid reasons for doing so. After all Bittrex earns when people trade and not by delisting coins

Nope, not necessary, they could have shady reasons too ;-) And there is nothing wrong at all with Metal... they simply do not want to support their competition LOL. Metal will go up without Bittrex too ;-) Check it up: https://steemit.com/crypto-news/@cryptoclick/breaking-news-re-metal-token-developments

Do some research on the coins they don't look legit to me so it's probably for good reasons they're being de listed. Here is my brief summary;

Every DGX = 1 Gram of gold. (Bold claims for an ICO)
MTL is also an ICO could be legit but I'm not sure
TRIG - Last post on twitter was in November

What is MTL? I do not fully understand this whole "Proof Of Payments Processed" as a means of securing a network.

MTL is a cryptocurrency for the Metal Payment processing platform which will speed up the cryptocoins mass adoption by providing a clean, friendly interface coupled with multiple membership incentives.

This is quoted from my post here: https://steemit.com/crypto-news/@cryptoclick/breaking-news-re-metal-token-developments
You are invited to read it and... get some Metal tokens

if they have decided to delist a coin it is more then likely because the team behind the coin is either having trouble or doing something shady.

After this discharge from the big platform, it is very likely that these currencies will fall to large levels
This may have a great impact on those who continue in it, so the currency team must intervene to find solutions

What will happend to my coins, if I don´t sell them and they will be delisted? Do I lose it?