This is what you want:

df1.groupby('User').apply(lambda df: df.sample(1))

Without the extra index:

df1.groupby('User', group_keys=False).apply(lambda df: df.sample(1))

Maybe:

def sample(chunk, rate=0.2):
    n = max(int(len(chunk)*rate), 1)

    return chunk.sample(n=n, replace=True, random_state=1)

df.groupby('month', group_keys=False).apply(sample)

IIUC, get the unique values, sample and slice with isin and boolean indexing:

from random import sample

out = df[df['User_ID'].isin(random.sample(list(df['User_ID'].unique()), 1000))]

You could use groupby.sample, either to pick out a sample of the whole dataframe for further processing, or to identify rows of the dataframe to mark if that's more convenient.

import pandas as pd

percentage_to_flag = 0.5

# Toy data: 8 rows, persons A and B.
df = pd.DataFrame(data={'persons':['A']*4 + ['B']*4, 'data':range(8)})
#   persons  data
# 0       A     0
# 1       A     1
# 2       A     2
# 3       A     3
# 4       B     4
# 5       B     5
# 6       B     6
# 7       B     7

# Pick out random sample of dataframe.
random_state = 41  # Change to get different random values.
df_sample = df.groupby("persons").sample(frac=percentage_to_flag,
                                         random_state=random_state)
#   persons  data
# 1       A     1
# 2       A     2
# 7       B     7
# 6       B     6

# Mark the random sample in the original dataframe.
df["marked"] = False
df.loc[df_sample.index, "marked"] = True
#   persons  data  marked
# 0       A     0   False
# 1       A     1    True
# 2       A     2    True
# 3       A     3   False
# 4       B     4   False
# 5       B     5   False
# 6       B     6    True
# 7       B     7    True

If you really do not want the sub-sampled dataframe df_sample you can go straight to marking a sample of the original dataframe:

# Mark random sample in original dataframe with minimal intermediate data.
df["marked2"] = False
df.loc[df.groupby("persons")["data"].sample(frac=percentage_to_flag,
                                            random_state=random_state).index,
       "marked2"] = True
#   persons  data  marked  marked2
# 0       A     0   False    False
# 1       A     1    True     True
# 2       A     2    True     True
# 3       A     3   False    False
# 4       B     4   False    False
# 5       B     5   False    False
# 6       B     6    True     True
# 7       B     7    True     True