In Bitcoin, the “local currency” equivalent to your “MyDogeCoin” example is called The lightning network.
Simplifying a bit to support your analogy:
Bitcoin lets you lock coins on the chain for a certain amount of time. Two people can do this, then trade bitcoin transactions back and forth without submitting them.
For example, I lock coins and give my coworker a bitcoin transaction I have signed giving him $10 worth of bitcoin for my share of the days lunch. Next day he fives me one for $13 for his share, and I give the restaurant $43 for the bill— all these transactions are literally trading bitcoin IOUs, but in a nearly trustless way.
This means a great deal of transactions can happen off chain without the risk of theft.
Simplifying a bit to support your analogy:
Bitcoin lets you lock coins on the chain for a certain amount of time. Two people can do this, then trade bitcoin transactions back and forth without submitting them.
For example, I lock coins and give my coworker a bitcoin transaction I have signed giving him $10 worth of bitcoin for my share of the days lunch. Next day he fives me one for $13 for his share, and I give the restaurant $43 for the bill— all these transactions are literally trading bitcoin IOUs, but in a nearly trustless way.
This means a great deal of transactions can happen off chain without the risk of theft.