Working with inaccurate (incorrect) dataset This is my problem description:

"According to the Survey on Household Income and Wealth, we need to find out the top 10% households with the most income and expenditures. However, we know that these collected data is not reliable due to many misstatements. Despite these misstatements, we have some features in the dataset which are certainly reliable. But these certain features are just a little part of information for each household wealth."

Unreliable data means that households tell lies to government. These households misstate their income and wealth in order to unfairly get more governmental services. Therefore, these fraudulent statements in original data will lead to incorrect results and patterns.

Now, I have below questions:

How should we deal with unreliable data in data science?
Is there any way to figure out these misstatements and then report the top 10% rich people with better accuracy using Machine Learning algorithms? -How can we evaluate our errors in this study? Since we have unlabeled dataset, should I look for labeling techniques? Or, should I use unsupervised methods? Or, should I work with semi-supervised learning methods?
Is there any idea or application in Machine Learning which tries to improve the quality of collected data?
Please introduce me any ideas or references which can help me in this issue.

Thanks in advance.
I have read @MaximHaytovich's answer and it is a good one. I would just like to suggest some further options, which were generalized in that answer as feature engineering. I would suggest trying to do the obvious first and analyze the data before transforming it to become ready for any machine learning algorithm. First look at the data and learn yourself and hypothesize about what patterns could be indicators of fraud. What is the nature of the data that you are 100% sure is reliable (it is mentioned in the question you posted that there is available data that is reliable) and how informative are they for the goal? The more familiar you are with the data, the better interpretation you can provide to any output you get from the methods you use. Try doing some outlier analysis on the incomes or any features that may be fraudulent that may make sense to do outlier detection on. Are there any suspicious missing values? Try doing clustering (one of the unsupervised algorithms you were talking about) to see if there are any in-betweens or irregularities.