Can duplicate examples create multi-collinearity? We know if any linear dependency exists in training data, therefore, the feature matrix becomes singular and hence, we cannot solve it. But apart from the features (columns), a matrix can still can be singular if it has duplicate rows. More specifically if we provide duplicate examples in training data this will happen. So, logically it should also create multi-collinearity problem. But it seems to me that this issue is underrated compared to the issue where the features are linearly dependent. Will not the linear dependency in rows create multi-collinearity problem? Does this case have another name? Correct me if I am mistaken. And if duplicate or linearly dependent rows exist and if they create problem, how to spot and fix this problem?

There is no problem with duplicate rows. Consider some applied examples, such as "returns to education", i.e., how much do people earn given their education, gender, experience etc. There can, and often will, be people in the dataset with the same gender, years of education and years of labor market experience. So there is also no fix necessary.
Note that multicollinearity implies that the regressor matrix does not have full column rank, which in turn is what we need for the $X'X$ matrix involved in the OLS estimator to be invertible, or, put differently, for all coefficients to be identifiable.
Finding duplicate rows, if still desired, might be done as follows:
set.seed(1)
n <- 10
education <- sample(10:15, n, replace=T)
gender <- sample(0:1, n, replace=T)

(X <- cbind(education, gender))

duplicated(X)

> (X <- cbind(education, gender))
      education gender
 [1,]        10      0
 [2,]        13      0
 [3,]        10      0
 [4,]        11      1
 [5,]        14      1
 [6,]        12      1
 [7,]        15      1
 [8,]        11      0
 [9,]        12      0
[10,]        12      0

> duplicated(X)
 [1] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE

